Warwick Mathematics Institute Events

Seminar List Entry | Seminars by subject

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Upcoming Seminars

Past Seminars

Number Theory on 23 June 2025 at 15:00

Speaker: Netan Dogra (Kings college)
Title: p-adic approaches to unlikely intersections.

Abstract: et C be a curve over the complex numbers. In this talk I will explain p-adic approaches to understanding the following numbers.

— The number of points P in C where f1(P),f2(P) and f3(P) lie in a one dimensional subspace of the multiplicative group of the complex numbers (here f1,f2 and f3 are meromorphic functions on C).
— The number of points P1 , ... , Pn in C such that there is a non-constant function on C with divisor supported on {P1 , ... , Pn } (joint work with Arnab Saha)
— The number of points P in C such that some nonzero multiple of P lies in a fixed finitely generated subgroup of the Jacobian of C (joint work with Sudip Pandit).

Time permitting, I will also discuss some generalisations.

Number Theory on 16 June 2025 at 15:00

Speaker: Oleksiy Klurman (University of Bristol)
Title: Short character sums and applications

Abstract: Understanding short character sums is a central problem in analytic number theory with numerous applications. I will talk about two recent results and how to apply them to study zeros of Littlewood-type polynomials and an averaged version of the Artin primitive root conjecture.

Combinatorics on 13 June 2025 at 14:00

Speaker: Rob Silversmith (Warwick)
Title: Chromatic polynomials in geometry

Abstract: The chromatic polynomial of a graph has a habit of showing up in unexpected places in geometry, e.g. in the theory of hyperplane arrangements. This sometimes has interesting purely combinatorial consequences, such as Huh's proof of Read's conjecture --- which uses algebraic geometry to show that the coefficients of the chromatic polynomial of any graph form a log-concave sequence. I'll discuss another surprising incarnation of chromatic polynomials, in the context of configuration spaces of points on the Riemann sphere. Interestingly, this leads naturally to a new definition of a "chromatic polynomial" for directed graphs, which remains mysterious but satisfies many nice combinatorial properties.

Number Theory on 09 June 2025 at 15:00

Speaker: Lilian Matthiesen (University of Gottingen)
Title: U^k-norms of smooth numbers

Abstract: An integer is called y-smooth if all of its prime factors are of size at most y. We will report on work in progress on the problem of bounding the U^k-norms of the set of y-smooth numbers below N. These sets are sparse as soon as y is sufficiently small, that is if y= N^{o(1)}, and yet they enjoy very good distributional properties. From a technical perspective, this problem is an interesting new test case for known techniques for studying U^k-norms, since, in particular, standard constructions for "pseudo-random majorants" are no longer available once y is sufficiently small.

Combinatorics on 06 June 2025 at 14:00

Speaker: Adva Mond (King's College London)
Title: Approximate Itai-Zehavi conjecture for random graphs

Abstract: The Itai-Zehavi conjecture states that every k-vertex-connected graph contains k vertex-independent spanning trees, that is, k spanning trees rooted at a common vertex r, such that for every vertex v the paths between r and v in different trees are internally vertex-disjoint. We show that with high probability the Itai-Zehavi conjecture holds asymptotically for the binomial random graph G(n,p) when np=ω(log n) and for the random regular graph G(n,d) when d= ω(log n).

This is a joint work with Lawrence Hollom, Lyuben Lichev, Julien Portier and Yiting Wang.

Number Theory on 02 June 2025 at 15:00

Speaker: Tom Fisher (University of Cambridge)
Title: TBA

Abstract: TBA

Combinatorics on 30 May 2025 at 14:00

Speaker: Daniel Kral (Leipzig University and MPI MiS)
Title: Curves on the torus with prescribed intersections

Abstract: Juvan, Malnič and Mohar [J. Combin. Theory Ser. B 68 (1996), 7-22] proved that for every surface S and every integer k, there exists N(S,k) such that any set of simple closed curves on the surface S, where any two are non-homotopic and intersect at most k times, has a maximum size at most N(S,k). In the case when S is the torus T^2, the problem has an interesting connection to number theory as the Riemann hypothesis yields that N(T^2,k)<=k+O(k^0.5*log k); Aougab and Gaster [Math. Proc. Cambridge Philos. Soc. 174 (2023), 569-584] proved N(T^2,k)<=k+O(k^0.5*log k) directly. We compute N(T^2,k) for every k and in particular show that N(T^2,k)<=k+6 for all k and N(T^2,k)<=k+4 when k is sufficiently large.

The talk is based on joint work with Igor Balla, Marek Filakovský, Bartłomiej Kielak and Niklas Schlomberg.

Statistical Mechanics on 29 May 2025 at 14:00

Speaker: Katarzyna Macieszczak (University of Warwick)
Title: TBOccupation Uncertainty Relations

Abstract: I will introduce occupation uncertainty relations (OURs) for dynamics of Markov processes over discrete configurations. OURs are lower bounds on fluctuations rates of system observables that are time integrated along stochastic trajectories. They correspond to a matrix bound on correlations between times spent in different system configurations, i.e., occupation times, which is expressed only in terms of stationary probabilities and lifetimes of individual configurations. It follows that any dynamics that saturates the bound is optimal in approximating stationary distribution by occupation times; I will demonstrate this always occurs for unidirectional cycles. I will also discuss how using OURs, dynamic correlations for a general Markov process can be asymptotically bounded in terms of static correlations, in turn leading to the positivity of dynamic exponents in the thermodynamic limit.

Geometry and Topology on 29 May 2025 at 13:30

Speaker: Daniele Turchetti (University of Durham)
Title: Non-Archimedean limits of families of Schottky groups

Abstract: Non-Archimedean analytic geometry provides a powerful framework for understanding families of geometric objects defined over the complex numbers. This perspective proves particularly fruitful when studying degenerations, compactifications, and limiting behaviors that are otherwise elusive in the Archimedean setting.
This talk aims to provide a gentle introduction to these techniques, with a particular focus on the case of Schottky spaces and moduli of curves, where recent work has highlighted deep connections between classical and non-Archimedean geometries. The final aim is to present joint work with Jérôme Poineau, in which we construct Schottky spaces over rings of integers of number fields and its connections with the outer space in geometric group theory. Finally, I will explain how these ideas have been used by Dang–Mehmeti and Li–Matheus–Pan–Tao to analyze the limiting behavior of Schottky groups and their associated spectra.

Number Theory on 27 May 2025 at 15:00

Speaker: Simon Baker (Loughborough University)
Title: TBA

Abstract: TBA

Statistical Mechanics on 22 May 2025 at 14:00

Speaker: Spyros Garouniatis (University of Warwick)
Title: Large systems of trapped Brownian motions with symmetrised initial and terminal conditions

Abstract: We study a model involving N Brownian motions over a fixed time interval [0,\beta], confined to a bounded spatial domain and subject to symmetrised boundary conditions. Specifically, the terminal position of the i-th Brownian motion is matched to the initial position of the \sigma(i)-th, where \sigma is a uniformly random permutation of {1,…,N}. This model arises naturally in quantum physics as a description of Boson systems at positive temperature 1/\beta, and the resulting probability distribution is known as the symmetrised measure. Using the framework of large deviations theory, we analyse the asymptotic behaviour of empirical path measures and average occupation measures as N becomes large, yielding insight into the limiting free energy of the system. We also investigate a connection with entropic optimal transport, specifically the Schrödinger bridge problem. In particular, we show that the minimiser of the rate function associated with the empirical path measure coincides with the solution to a Schrödinger bridge problem.

Number Theory on 19 May 2025 at 15:00

Speaker: Andy Booker (University of Bristol)
Title: L-functions from nothing

Abstract: Long before the proof of the modularity theorem, evidence for it was amassed in the 1972 "Antwerp IV" tables comparing elliptic curves and modular forms of small conductor; in particular, D. J. Tingley's calculation of spaces of modular forms was essential for filling some gaps in the elliptic curve table, and gave a de facto complete list of all elliptic curves of conductor up to 200. In the decades that followed this list was extended by John Cremona and is now a major part of the L-functions and Modular Forms Database (LMFDB).

Elliptic curves are abelian varieties of dimension 1. In recent decades similar efforts have been undertaken in dimension 2, including a 2015 tabulation of genus 2 curves corresponding to abelian surfaces which can be found in the LMFDB. But we lack an analogue of Tingley's table of modular forms, and with it any proof of completeness or evidence of gaps. Directly computing the relevant spaces of modular forms is prohibitively difficult, even for small conductors.

In the talk I will describe joint work with Andrew Sutherland extending a method of Farmer, Koutsoliotas, and Lemurell that makes it possible to compute these spaces indirectly. The result is a provably complete tabulation of L-functions of modular forms of conductor up to 1368, and partial results for some conductors as large as 2401. For instance, we obtain a complete classification of modular abelian surfaces with good reduction away from 7.

Combinatorics on 16 May 2025 at 14:00

Speaker: Luca Sabatini (University of Warwick)
Title: Breaking symmetry of symmetric objects

Abstract: Let $G$ be a permutation group on the finite set $\Omega$. One of the most studied topics in permutation group theory is finding a partition of $\Omega$ whose stabiliser is trivial. This means fixing a limited amount of points or subsets which fix all $\Omega$. Here we consider a small variation: we fix only the bare minimum (so one subset, or a pair of points) and we do not aim to find a trivial stabiliser, since this would be impossible in general, but to find a stabiliser that has at least some good properties.

Tropical Mathematics LMS Network Meeting on 15 May 2025 at 16:30

Speaker: Alexander Esterov (LIMS)
Title: Schön complete intersections

Abstract: There is a number of "aesthetically similar" topics in combinatorial algebraic geometry, such as toric complete intersections, hyperplane arrangements, simplest singularity strata of general polynomial maps, some discriminant and incidence varieties in enumerative geometry and polynomial optimization, polynomial ODEs such as reaction networks, generalized Calabi--Yau complete intersections.

I will talk about a convenient umbrella generality for all of them, which still admits a version of the classical theory of Newton polytopes (but with so-called tropical complete intersections instead of polytopes).

Tropical Mathematics LMS Network Meeting on 15 May 2025 at 15:00

Speaker: Stefano Mereta (KTH)
Title: The space of valuated preorders and the congruence spectrum of S[x1,…,xn] as the spectrum of a ring

Abstract: In the late '60s, Hochster introduced the notion of spectral space and proved that every spectral space is the spectrum of a commutative ring. Unfortunately the proof of this fact is not constructive. More recently, Jun, Ray and Tolliver have proven constructively that every spectral space is the k-spectrum of an idempotent semiring, and that the congruence spectrum of an idempotent semiring is a spectral space.

In this talk we will introduce the notion of a valuated preorder on the monomials of K[x1,…,xn] for a valued field K and realise it, relying partially on work by Jóo and Mincheva, as the k-spectrum of a semiring, as the congruence spectrum of a polynomial semiring and, most importantly, as the spectrum of a commutative ring.

This commutative ring is constructed as the "unit ball" of respect a generalised Bézout valuation.

Geometry/Topology + Tropical Mathematics LMS Network Meeting on 15 May 2025 at 13:30

Speaker: Hannah Markwig (Tübingen)
Title: Tropical curve counting

Abstract: In enumerative geometry, we fix geometric objects and conditions and count how many objects satisfy the conditions. For example, there are 2 plane conics passing through 4 points and tangent to a given line. Tropical geometry can be viewed as a degenerate version of algebraic geometry and has proved to be a successful tool for enumerative problems. We review tropical curve counting problems. In particular, we show how tropical methods can be applied for quadratically enriched counts, which can be viewed as generalizations that allow results over any ground field.

Geometry and Topology on 15 May 2025 at 13:30

Speaker: Hannah Markwig (University of Tübingen)
Title: Tropical Curve Counting

Abstract: In enumerative geometry, we fix geometric objects and conditions and count how many objects satisfy the conditions. For example, there are 2 plane conics passing through 4 points and tangent to a given line. Tropical geometry can be viewed as a degenerate version of algebraic geometry and has proved to be a successful tool for enumerative problems. We review tropical curve counting problems. In particular, we show how tropical methods can be applied for quadratically enriched counts, which can be viewed as generalizations that allow results over any ground field.

Number Theory on 12 May 2025 at 15:00

Speaker: Joni Teravainen (University of Cambridge)
Title: Linnik's problem for the Möbius function

Abstract: We show that the least natural number having an odd number of prime factors and belonging to any arithmetic progression a mod q is bounded by q^{2+o(1)}. This can be seen as a multiplicative analogue of Linnik's problem on the least prime in an arithmetic progression. This is joint work with Kaisa Matomäki.

Geometry and Topology on 08 May 2025 at 13:30

Speaker: Anna Felikson (University of Durham)
Title: Hyperbolic geometry of friezes

Abstract: Frieze patterns were introduced by Coxeter in the 1970s who, with Conway, established a correspondence between frieze patterns and triangulated polygons. It turned out later that this object is very rich in connections with different fields in mathematics. We use hyperbolic geometry to provide a classification of positive integral friezes on marked bordered surfaces. This is a joint work with Pavel Tumarkin.

Number Theory on 28 April 2025 at 15:00

Speaker: Victor Flynn (University of Oxford)
Title: An Abelian Surface Analog of Edwards Curves

Abstract: In 2007, Edwards described a parametrised model of elliptic curves for which there is a universal group law; that is to say, there is a single algebraic expression which covers all possibilities for P + Q, regardless of whether P,Q are distinct, the same, negatives of each other, and so on. This is subject to two conditions: the existence of a point of order 4 over the ground field, and an arithmetic condition on the parameter, that it is nonsquare. This was in contrast to the standard Weierstrass model normally given in textbooks, which require a number of different algebraic expressions for these cases. Edwards curves have attracted a substantial literature, and various researchers have investigated related twists and isogenies. In this talk, I shall describe joint work with Kamal Makdisi, in which we have developed an analogous model in P^3 x P^3 for Jacobian varieties of curves of genus 2.

Combinatorics on 25 April 2025 at 14:00

Speaker: Asaf Cohen Antonir (Tel Aviv University)
Title: Weak saturation and collapsible complexes in a random graph

Abstract: Let H, G be two graphs. A spanning subgraph G’ of G is called weakly H-saturated if the following holds: one can add to G' the edges of G \ G’ in some order so that whenever a new edge is added, a new copy of H is formed. Obtaining lower bounds for the size of such a G’ (for various H and G) is a classical problem in extremal combinatorics. In particular, in the past 40 years, various algebraic tools have been used in order to prove such lower bounds. Our first contribution in this work unravels a new algebraic/topological connection which can be used in order to prove the following result. Let w-sat(t,G) be the size of a smallest weakly K_t-saturating subgraph of G.
Korandi and Sudakov asked to determine the threshold probability for the property that w-sat(t,G(n,p))=w-sat(t,K_n). Using our new observation, in the case t=3, we show that the threshold probability is located at p=n^{-1/3 +/- o(1)}. Moreover, using an argument inspired by Gromov's `local to global' theorem, we determine, up to a multiplicative constant factor, the threshold probability for a bounded diameter version of the theorem.

Interestingly, our new connection between weak saturation and topological properties goes both ways since it also enables us to use combinatorial arguments in order to obtain new results concerning topological properties of random clique complexes. In particular, we obtain a new upper bound on the threshold probability for simple connectivity of the 2-dimensional clique complex of G(n,p), improving a result of Khale.

Joint work with Yuval Peled, Asaf Shapira, Mykhaylo Tyomkyn, and Maksim Zhukovskii.

Geometry and Topology on 20 March 2025 at 13:30

Speaker: Macarena Arenas (University of Cambridge)
Title: Taut smoothings and shortest geodesics

Abstract: In this talk we will discuss the connection between combinatorial properties of minimally self-intersecting curves on a surface S and the geometric behaviour of geodesics on S when S is endowed with a Riemannian metric. In particular, we will explain the interplay between a smoothing, which is a type of surgery on a curve that resolves a self-intersection, and k-systoles, which are shortest geodesics having at least k self-intersections, and we will present some results that partially elucidate this interplay.

Combinatorics on 14 March 2025 at 14:00

Speaker: Shoham Letzter (University College London)
Title: Almost covering regular graphs by F-subdivisions

Abstract: A conjecture of Verstraëte from 2002 asserts that for every graph F there exists d such that every regular graph with degree at least d has a collection of pairwise vertex-disjoint subdivisions of F covering almost all the vertices in the graph. We prove this conjecture for regular n-vertex graphs with degree at least (log n)^{130}. Along the way we develop useful tools related to almost regular expanders. This is joint work with Abhishek Methuku and Benny Sudakov.

Soft Matter Lunches on 12 March 2025 at 13:00

Speaker: Mingchao Liu (University of Birmingham)
Title: TBA

Abstract: TBA

Combinatorics on 11 March 2025 at 15:00

Speaker: Maksim Zhukovskii (University of Sheffield)
Title: The sharp threshold for the square of a Hamilton cycle

Abstract: In 2020, Kahn, Narayanan, and Park conjectured that the probability threshold for the binomial random graph G(n,p) to contain the square of a Hamilton cycle is (1+o(1))\sqrt{e/n}. In the talk, I will present a proof of this conjecture. Although the proof relies on the fragmentation technique, as the original proof by Kahn, Narayanan and Park for establishing a coarse threshold, the way of selecting fragments is essentially different. One of the main ingredients of the proof is the fact that sufficiently many squares of cycles have fragments that avoid squares of paths of length at least logarithmic in n with high probability.

Partial Differential Equations and their Applications on 11 March 2025 at 12:00

Speaker: Yohance Osborne (Durham University)
Title: Analysis and Numerical Approximation of Mean Field Game Partial Differential Inclusions

Abstract: The Mean Field Game (MFG) system of Partial Differential Equations (PDE), introduced by Lasry & Lions in 2006, models Nash equilibria of large population stochastic differential games of optimal control where the players of the game have unique optimal controls, and the convex Hamiltonian of the underlying optimal control problem is differentiable. In this talk, we introduce a new class of model problems called Mean Field Game Partial Differential Inclusions (MFG PDI), which extend the MFG system of Lasry and Lions to situations where players may have possibly nonunique optimal controls, and the resulting Hamiltonian of the underlying optimal control problem is not required to be differentiable. We prove the existence of unique weak solutions to MFG PDI for a broad class of Hamiltonians that are convex, Lipschitz, but possibly nondifferentiable, under a monotonicity condition similar to one considered previously by Lasry & Lions. Moreover, we introduce a class of monotone finite element discretizations of the weak formulation of MFG PDI and present theorems on the strong convergence of the approximations to the value function in the $L^2(H_0^1)$-norm and the strong convergence of the approximations to the density function in $L^p(L^2)$-norms. We conclude the presentation with discussion of a numerical experiment involving a non-smooth solution.

Number Theory on 10 March 2025 at 15:00

Speaker: Oleksiy Klurman (University of Bristol)
Title: SEMINAR POSTPONED DUE TO SPEAKER ILLNESS

Abstract: .

Combinatorics on 07 March 2025 at 14:00

Speaker: Andrew Treglown (University of Birmingham)
Title: Arbitrary orientations of Hamilton cycles in directed graphs

Abstract: In 1960, Ghouila-Houri proved that every strongly connected directed graph G on n vertices and with minimum degree at least n contains a directed Hamilton cycle. We asymptotically generalize this result by proving the following: every directed graph G on n vertices and with minimum degree more than (1+o(1))n contains every orientation of a Hamilton cycle, except for the directed Hamilton cycle in the case when G is not strongly connected. This is joint work with Louis DeBiasio.

Number Theory on 07 March 2025 at 13:00

Speaker: David Masser (Basel)
Title: TBA

Abstract: TBA

Analysis on 06 March 2025 at 16:00

Speaker: Paul Minter (Cambridge)
Title: Stable Minimal Hypersurfaces in \R^5

Abstract: I will discuss why every complete two-sided stable minimal hypersurface in \R^5 is flat, resolving the so-called ‘stable Bernstein problem’ in this dimension. The proof utilises both ideas from comparison geometry (through their spectral counterparts) as well as Gromov’s \mu-bubbles. This is based on joint work with Otis Chodosh, Chao Li, and Douglas Stryker.

Geometry and Topology on 06 March 2025 at 13:30

Speaker: Ismael Morales (University of Oxford)
Title: Fixed points, splittings and division rings

Abstract: Let G be a free group of rank N, let f be an automorphism of G and let Fix(f) be the corresponding subgroup of fixed points. Bestvina and Handel showed that the rank of Fix(f) is at most N, for which they developed the theory of train track maps on free groups. Different arguments were provided later on by Sela, Paulin and Gaboriau-Levitt-Lustig. In this talk, we present a new proof which involves the Linnell division ring of G. We also discuss how our approach relates to previous ones and how it gives new insight into variations of the problem.

Partial Differential Equations and their Applications on 04 March 2025 at 12:00

Speaker: Iwona Chlebicka (University of Warsaw)
Title: Asymptotics for the Cauchy problem for the fast p-Laplace evolution equation

Abstract: We focus on the fast diffusion equation involving p-Laplacian for p<2. The properties of the solutions to the p-Laplace Cauchy problem change in several special values of the parameter p. In the range of p when mass is conserved, non-negative solutions behave like the Barenblatt (or fundamental) solutions for large times. The convergence was established in the literature for p close to 2, but no rates were available. We show the polynomial rates of the convergence in the uniform relative error for a natural class of initial data. In particular, we allow for the values of p, for which the entropy is not displacement convex, placing our study outside of the reach of the optimal transportation tools. Joint project with Matteo Bonforte and Nikita Simonov, arXiv:2405.05405.

SBIDER on 03 March 2025 at 14:00

Speaker: Joaquin Prada (University of Surrey)
Title: Multidisciplinary approaches to inform sustainable public health policy: The example of Cystic Echinococcosis

Abstract: Mathematical modelling has been used extensively to inform public health, particularly to capture the dynamics of infectious diseases in populations and explore possible mitigation strategies. However, to provide sustainable policy recommendations that can be maintained in the long-term, integration with other disciplines is required. In this talk, a few examples of integration of mathematical modelling with other disciplines will be discussed in the context of Cystic Echinococcosis (a neglected parasitic zoonosis).

Combinatorics on 28 February 2025 at 14:00

Speaker: Nora Frankl (Open University)
Title: The Quantitative Helly Theorem

Abstract: Helly's theorem states that if the intersection of any d+1 members of a finite family F of convex sets in R^d is nonempty, then the intersection of the whole family is nonempty. The Fractional Helly theorem of Katchalski and Liu, and the Quantitative Helly theorem of Bárány, Katchalski, and Pach are two famous extensions of this result. Improving on several recent works, we prove an optimal combination of these two extensions. We show that if a positive fraction of the (d+1)-tuples of F intersect in large volume, then a positive fraction of F intersects in large volume as well. Joint work with Attila Jung and Istvan Tomon.

Statistical Mechanics on 27 February 2025 at 14:00

Speaker: Henrik Ueberschär (Sorbonne Université)
Title: Multifractality for periodic solutions of certain PDE

Abstract: Many dynamical systems are in a state of transition between two regimes. Examples are firing patterns of neurons, disordered quantum systems or pseudo-integrable systems. A common feature which is often observed for critical states of such systems is a multifractal self-similarity in a certain scaling regime which cannot be captured by a single fractal exponent but only by a spectrum of fractal exponents.I will discuss a proof of multifractality of solutions for certain stationary Schrödinger equations with a singular potential on the square torus (joint with Jon Keating). Towards the end of the talk, I will allude to some new work on multifractal scaling and solutions to nonlinear PDE in fluid dynamics on cubic tori.

Probability Theory on 26 February 2025 at 16:00

Speaker: Luca Fresta (University of Bonn)
Title: Density of States of Random Band Matrices close to the Edge of the Spectrum

Abstract: We study the random band matrix ensemble introduced by Disertori--Pinson--Spencer, characterised by the variance profile associated with the operator $(-W^{2}\Delta_{\mathbb{Z}^{3}}+1)^{-1}$, $\Delta_{\mathbb{Z}^{3}}$ being the Laplacian on the three-dimensional lattice and $W$ being the characteristic width of the band. For any energy $E$ close to the edge of the spectrum, namely for $1.8 <|E| <2$, we rigorously prove that the density of states follows Wigner’s semicircle law with power law corrections in $W^{-1}$, provided $W$ is sufficiently large, depending on $E$. The proof relies on the supersymmetric approach of Disertori--Pinson--Spencer, and extends their result, which was previously established for energies $|E| \leq 1.8$. Joint work with M. Disertori.

Partial Differential Equations and their Applications on 25 February 2025 at 12:00

Speaker: Tom Sales (University of Warwick)
Title: Topics on the Navier-Stokes equations on evolving domains

Abstract: In physics and biology one may obtain models of physical phenomena involving partial differential equations posed on evolving domains, which may or may not be known a priori. In this talk we discuss some problems related to the Navier-Stokes equations posed on evolving domains. Firstly, we discuss recent results concerning the derivation and well-posedness of a Navier-Stokes-Cahn-Hilliard system posed on an evolving surface with prescribed evolution. Secondly, we outline a new, constructive approach to a fluid-rigid body interaction problem with no slip boundary conditions. This approach is based on an iteration of problems posed on prescribed evolving domains. This talk is based on joint works with Charles Elliott.

Number Theory on 24 February 2025 at 15:00

Speaker: Shin-ya Koyama (Toyo University)
Title: Weighted Prime Number Theorem with Refinements

Abstract: For $s \geq 0$, the weighted counting functions for primes $p$ with weight $p^{-s}$ are defined as $$ \pi_s(x) = \sum_{p \leq x} p^{-s}, \quad \pi_s(x, q, a) = \sum_{\substack{p \equiv a \ (\text{mod} \ q) \\ p \leq x}} p^{-s}. $$ When $s = 0$, they agree to the classical counting functions $\pi(x)$ and $\pi(x, q, a)$. In 2023, Aoki and Koyama proved under the Deep Riemann Hypothesis for Dirichlet $L$-functions that \begin{equation*} \pi_s(x, q, b) - \pi_s(x, q, a) = \begin{cases} c_q \log \log x + O(1), & (x \to \infty, s = \frac{1}{2}) \\ O(1), & (x \to \infty, s > \frac{1}{2}) \end{cases} \end{equation*} for any $a \in (\mathbb{Z}/q\mathbb{Z})^{\times 2}$, $b \in (\mathbb{Z}/q\mathbb{Z})^{\times} \setminus (\mathbb{Z}/q\mathbb{Z})^{\times 2}$, with $c_q$ the number of real Dirichlet characters mod $q$ divided by $2 \varphi(q)$. A new formulation of Chebyshev’s bias was given by the asymptotic at $s = 1/2$. When $s = 0$, Littlewood (1914) proved that both $\pi(x) - \text{Li}(x)$ and $\pi(x, q, a) - \pi(x, q, b)$ are unbounded changing their signs infinitely many times. But the results for $0 < s < 1/2$ were unknown. In this talk, after proving the weighted prime number theorem $\pi_s(x) \sim \text{Li}(x^{1-s})$ as $x \to \infty$, we show that both $\pi_s(x) - \text{Li}(x^{1-s})$ and $\pi_s(x, q, a) - \pi_s(x, q, b)$ are also unbounded changing their signs infinitely many times if $0 < s < 1/2$. This is a generalization of Littlewood’s theorem, and justifies our formulation of Chebyshev’s bias which refers to the exact weight at $s = 1/2$. This is joint work with Koji Shimada.

SBIDER on 24 February 2025 at 14:00

Speaker: Reiko Tanaka (Imperial College London)
Title: Mechanistic modelling of allergic diseases – From mechanisms to prediction

Abstract: In this talk, I will showcase our group’s recent works, including mechanistic modelling and machine learning/AI methods towards designing personal treatment strategies for allergic diseases (eczema, asthma). For example, we developed a mechanistic model of eczema pathogenesis which provides a coherent mechanistic explanation of the dynamic onset, progression, and prevention of eczema. The model describes triangle interactions between skin barrier, immune responses and environmental stressors. We further expanded the mechanistic models to include the effects of skin microbiome, which plays a crucial role in eczema pathogenesis. I would also like to touch on the current challenges of in silico modelling approach.

Combinatorics on 21 February 2025 at 14:00

Speaker: Sandra Albrechtsen (Hamburg University)
Title: Asymptotic and diverging half- and full-grid minors

Abstract: Georgakopoulos and Hamann [2024] showed that every locally finite, quasi-transitive graph G that is not quasi-isometric to a tree contains the full-grid as a minor. In this talk I discuss how this result could be strengthened so that the full-grid minor appears in the coarse (`large-scale') geometry of G. For this, I define asymptotic minors and diverging minors and describe how the full-grid can be found as such minors in G if G has the additional property that its cycle space is generated by cycles of bounded length. In particular, it follows that all locally finite Cayley graphs of finitely presented groups that are not virtually free contain the full-grid as an asymptotic minor and as a diverging minor. Additionally, I discuss assumptions which ensure that a (not necessarily quasi-transitive) graph contains the half-grid as an asymptotic minor and as a diverging minor. This is based on joint work with Matthias Hamann.

COW on 20 February 2025 at 17:00

Speaker: Anya Nordskova (Hasselt)
Title: Bondal-Polishchuk’s conjecture for Fano threefolds of Picard rank one

Abstract: TBA

COW on 20 February 2025 at 16:00

Speaker: Naoki Koseki (Liverpool)
Title: Degree two Gopakumar-Vafa invariants of local curves

Abstract: TBA

COW on 20 February 2025 at 14:15

Speaker: Karim Adiprasito (Jussieu and Hebrew University)
Title: Semigroup algebras, character rings and Parseval-Rayleigh identities

Abstract: TBA

COW on 20 February 2025 at 14:00

Speaker: Karim Adiprasito (Jussieu and Hebrew University)
Title: Semigroup algebras, character rings and Parseval-Rayleigh identities

Abstract: TBA

Statistical Mechanics on 20 February 2025 at 14:00

Speaker: Peter Gracar (University of Leeds)
Title: Lipschitz cutset for fractal graphs and applications to the spread of infections

Abstract: For Bernoulli supercritical percolation on the $d$-dimensional lattice it is well understood that the infinite component exists “everywhere”. In fact, it can be shown that this component contains as a subset a Lipschitz connected hyper-surface that can be built along any of the $d-1$ possible canonical hyperplanes of $mathbb{Z}^d$. In this talk, we will explain how one can construct a set satisfying similar properties on the Sierpiński gasket and then show how a multi-scale construction can be used to get its existence even for particle dependent percolation. More precisely, we will consider the fractal Sierpiński gasket or carpet graph in dimension $dgeq 2$, denoted by $G$. At time $0$, we place a Poisson point process of particles onto the graph and let them perform independent simple random walks, which in this setting exhibit sub-diffusive behaviour. We will generalise the concept of particle process dependent Lipschitz percolation to the (coarse graining of the) space-time graph $G imes mathbb{R}$, where the opened/closed state of space-time cells is measurable with respect to the particle process inside the cell. We will discuss an application of this generalised framework through the following: if particles can spread an infection when they share a site of $G$, and if they recover independently at some rate $gamma>0$, then if $gamma$ is sufficiently small, the infection started with a single infected particle survives indefinitely with positive probability.

Geometry and Topology on 20 February 2025 at 13:30

Speaker: Rachael Boyd (University of Glasgow)
Title: TBA

Abstract: TBA

Combinatorics on 19 February 2025 at 15:00

Speaker: Karim Adiprasito (Jussieu Institute of Mathematics - Paris Rive Gauche)
Title: (Open) Extremal problems in combinatorics and algebra

Abstract: Algebraic combinatorics and extremal combinatorics are, sadly, almost disjoint. Algebraic combinatorics deals with isomorphisms, and is an exact science. Extremal combinatorics is a study of a more quantitative nature. Hence, marrying the two is difficult. I will outline several problems that attempt to quantify "algebraic" results and present some results and open problems. This talk is more of a challenge with many open problems rather than results :)

Partial Differential Equations and their Applications on 18 February 2025 at 12:00

Speaker: Daniel Pezzi (Johns Hopkins University)
Title: Sharp spectral projection estimates for the torus

Abstract: It is a natural, but oftentimes difficult, question to deduce information about a periodic function from its Fourier series expansion. Spectral projection estimates are one way to explore this connection. If a function has its spectrum contained in an annulus, how large can the function be in an L^p norm? For unit width annuli this question is answered by the universal estimates of Sogge. If the projection operator projects onto an eigenspace, this is the Discrete Restriction conjecture of Bourgain. We present sharp estimates for intermediate cases for a large subset of the relevant parameters, which addresses a conjecture of Germain and Myerson. We will discuss the techniques used, similarities and differences to the case of general manifolds, and potential future avenues of attack.

Number Theory on 17 February 2025 at 15:00

Speaker: Robert Wilms (Caen)
Title: An algebraic approach to (arithmetic) intersection theory

Abstract: Intersection theory is a fundamental tool that provides a good measure of complexity, such as the degree of an algebraic variety or the height in Diophantine geometry, while being very compatible with most geometric constructions. In this work-in-progress talk I will present a new intersection theory of norms on rings using purely algebraic means. It provides a generalisation and at the same time a completely unified formulation of the geometric and arithmetic intersection theory of line bundles. It also provides potential applications in other areas of mathematics, such as discrete geometry or the theory of modular forms, which I will also discuss.

DAGGER on 17 February 2025 at 14:00

Speaker: Beno Učakar (University of Ljubljana)
Title: A beginner's guide to quasiconformal folding

Abstract: In 2014, Christopher J. Bishop pioneered a technique called quasiconformal folding, which, on a given domain, allows us to construct families of quasiconformal maps with uniformly controlled dilatations. This is done by adding tree-like structures to the domain's boundary. The inverses of these maps will take the boundary of the codomain and fold it onto itself to create these tree-like structures, hence the name quasiconformal folding. This technique turned out to be very powerful and was used to prove many results in complex dynamics, approximation theory, and the study of maps of bounded and finite type. Sadly, the original proof of the main tool in quasiconformal folding, the folding lemma, is rather daunting and hard to wrap your head around. My goal for this talk is to give some intuition behind quasiconformal folding, show why it might be useful, and go over the details of the proof of the folding lemma in a slightly simpler setting, where our domain is the outside of the unit disc.

SBIDER on 17 February 2025 at 14:00

Speaker: Michael Head (University of Southampton)
Title: Neglected tropical diseases, vaccine hesitancy, and entering the Chief’s Palace: health needs, challenges and anecdotes around Last Mile populations in rural Ghana

Abstract: This talk will cover Michael’s experiences of Ghana. He’ll cover the importance of equity in research and community entry when considering research in rural settings, including the difficulty of maintaining a squat greeting position and the taste of cola nuts. Then, he’ll move onto describing some of his research results, covering vaccine trust and hesitancy across the pandemic. This includes some findings around skin-related Neglected tropical diseases in both Ghana and neighbouring Togo, including healthcare seeking behaviour and bypassing of health facilities. The vaccine hesitancy research indicates belief in conspiracy theories, along with the role of politics as the basis of trust in public health messaging. Michael will cover the new UKRI inter-disciplinary grant, led by Professor Robin Goodwin at Warwick, that bring together psychologists, modellers, epidemiologists and drama experts to understand hotspots for infectious disease transmission in marketplaces in Ghana and Thailand. Michael will also cover the outreach project that takes two Southampton medical students to northern Ghana each year, along with brief reflections on his communications and media work during the pandemic (that includes the insistence of media crews filming him feeding the goldfish in his pond at home). He’s rather enjoying working with Warwick colleagues, so is keen to explore any new avenues for collaboration.

Combinatorics on 14 February 2025 at 14:00

Speaker: Marc Distel (Monash University)
Title: Further improvements to the product structure extension of the Alon-Seymour-Thomas theorem

Abstract: Alon, Seymour, and Thomas [1990] showed that every $n$ vertex graph that excludes $K_t$ as a minor has treewidth and pathwidth at most $O_t(\sqrt{n})$. Distel, Dujmović, Eppstein, Hickingbotham, Joret, Micek, Morin, Seweryn, and Wood [2024] expanded on this, showing that these graphs could be written as a $O_t(\sqrt{n})$-blowup of a treewidth 4 graph. I further refine this, by showing that the treewidth 4 can be replaced by treewidth 3, and can be further reduced to pathwidth 2 if you allow the blowup to have size $O_t(\sqrt{n}\log(n)^2)$.

Analysis on 13 February 2025 at 16:00

Speaker: Julian Weigt (Warwick)
Title: Alberti representations, rectifiability, PDEs and multilinear Kakeya

Abstract: We discuss connections between rectifiability, Alberti representations, regularity of solutions to a PDE and multilinear Kakeya. More precisely, we quantify a qualitative PDE regularity result by Guido DePhilippis and Filip Rindler, and use it show that sets with n independent Alberti representations are n-rectifiable, based on a prior result of David Bate and Sean Li. The quantitative PDE regularity result also implies a perturbation of a particular case of the Lipschitz multilinear Kakeya inequality, a delicate inequality that is known to hold in some important cases but fails in general. This is joint work with David Bate.

Mathematics Teaching and Learning on 13 February 2025 at 16:00

Speaker: Giulio Cesare Ardito (Manchester)
Title: Generative AI in Higher Education: a benefit to students, a challenge for educators

Abstract: Generative AI is rapidly integrating into student learning, improving accessibility, feedback, and engagement. However, this same technology disrupts traditional assessment methods and challenges the role of teachers and lecturers. As AI tutoring systems become more sophisticated, this talk explores the dual impact of generative AI: its capacity to enhance student learning when properly guided, and its groundbreaking impact on our education models. As AI shifts the balance of knowledge production, we must reconsider what—and how—we assess, and what remains uniquely human in the educational process.

Algebraic Geometry on 12 February 2025 at 15:00

Speaker: Nicholas Proudfoot (University of Oregon)
Title: The Schubert variety of a hyperplane arrangement

Abstract: I’ll tell you about some of my favorite algebraic varieties, which are beautiful in their own right, and also have some dramatic applications to algebraic combinatorics. These include the top-heavy conjecture (one of the results for which June Huh was awarded the Fields Medal), as well as non-negativity of Kazhdan—Lusztig polynomials of matroids.

Partial Differential Equations and their Applications on 11 February 2025 at 12:00

Speaker: Amélie Loher (University of Cambridge)
Title: Decay estimates for weak solutions of the Boltzmann equation

Abstract: We introduce a suitable notion of weak solutions to the Boltzmann equation on bounded space domains. In case of moderately soft and hard potentials, we show that these solutions decay pointwisely at any polynomial rate in velocity, provided that the mass, energy and entropy of the solutions are bounded. This is joint work with Cyril Imbert.

Number Theory on 10 February 2025 at 15:00

Speaker: Jessica Alessandri (Bath)
Title: TBA

Abstract: TBA

SBIDER on 10 February 2025 at 14:00

Speaker: Rebecca Hoyle (University of Southampton)
Title: MELD-B: clustering burden indicators in routine healthcare data

Abstract: In this talk I will introduce MELD-B, a large multidisciplinary multi-institution project that aims to use AI and mathematical modelling to analyse routine healthcare data and birth cohort datasets to characterise typical timelines for acquisition of multiple long-term health conditions through a person’s lifetime along with the types of burden that they experience as a result. We are using clustering methods to group together burdensome features that people experience as a result of their health conditions and learn what predicts particular patterns of burden. We aim to combine information from large GP and hospital healthcare datasets with rich information on early life from birth cohort datasets to uncover the early roots of later ill health and so identify potential timepoints for intervention and prevention. I will present preliminary clustering results for patterns of burden and the common conditions that are over-represented in the clusters. I will also outline our approach to modelling the trajectories of acquisition of long-term conditions and burdensome features.

Combinatorics on 07 February 2025 at 14:00

Speaker: Sayan Mukherjee (University of Tokyo)
Title: Spectral graph clustering and local differential privacy

Abstract: Finding clusters in graphs is an important problem in social network analysis. Of the many ways of finding such clusters, spectral clustering is widely used for the ease of implementation and its approximation guarantees via the Cheeger inequalities. However, simply publishing information about clusters in a social network leads to leakage in privacy. In a locally differentially private graph algorithm, users locally perturb their adjacency data before sending it to a central server, which then makes some inference on the perturbed graph. With proper addition of noise, it can be possible to protect users' privacy while still making statistical inference about the underlying social networks. In this talk, we will analyze the robustness of the spectral clustering algorithm under the addition of noise in the adjacency information.

Mathematics Teaching and Learning on 06 February 2025 at 16:00

Speaker: Richard Gratwick (Edinburgh)
Title: Flipped Classrooms and Interactive Learning at Edinburgh

Abstract: The University of Edinburgh School of Mathematics puts high importance on interactivity in its teaching. For many years, the "flipped classroom" model has been the basis for its teaching in the earlier years of the undergraduate programmes. Higher-level courses also use a variety of techniques to engage students in the classroom. In this talk I will give an overview of some of these approaches to teaching from the point of view of the practitioner at the chalkface. I shall discuss the practical implementation of these techniques, the advantages and disadvantages, and student and staff reactions that one often encounters.

Statistical Mechanics on 06 February 2025 at 14:00

Speaker: Gabriel Berzunza-Ojeda (University of Liverpool)
Title: Convergence of the Aldous-Broder Markov chain on high-dimensional regular graphs

Abstract: The Brownian continuum random tree emerges as a fundamental limit shape for various discrete tree models. It arises as the scaling limit of, for instance, the uniform spanning tree on the complete graph with $N$ vertices or on the torus $\mathbb{Z}^d_N$ of size-length $N$, for $d\geq 5$ (Peres and Revelle (2005)). Furthermore, the study of uniform spanning trees on connected graphs exhibits deep connections to several other key areas within probability theory. These include loop-erased random walks, potential theory, conformally invariant scaling limits, domino tilings, the Abelian sandpile model, and Sznitman's interlacement process. The Aldous-Broder Markov chain is a simple algorithm for generating random spanning trees. This Markov chain, defined on a graph $G=(V,E)$, evolves through a sequence of rooted trees, each with a subset of $V$ as its vertex set. In Evans, Pitman and Winter (2006), it was shown that the suitable rescaled Aldous-Broder Markov chain on a complete graph converges to the so-called root growth with regrafting process (RGRG process) weakly with respect to the Gromov-Hausdorff topology. In this talk, we study the convergence of the rescaled Aldous-Broder Markov chain on high-dimensional regular graphs, such as $\mathbb{Z}^d_N$, towards the RGRG process. Joint work with Osvaldo Angtuncio-Hernandez (Centro de Investigacion en Matematicas (CIMAT)) and Anita Winter (Universitat Duisburg-Essen).

Partial Differential Equations and their Applications on 04 February 2025 at 12:00

Speaker: Klaus Widmayer (University of Zurich)
Title: Landau damping near the Poisson equilibrium in R^3

Abstract: While "Landau damping" is regarded as an important effect in the dynamics of hot, collisionless plasmas, its mathematical understanding is still in its infancy. In particular, the terminology has evolved to include several types of (stabilizing) effects in diverse physical contexts, the mathematical description of which can differ markedly between various settings of relevance. This talk presents a recent nonlinear stability result for the homogeneous "Poisson" equilibrium of the Vlasov-Poisson equations on R^3, which relies on a combination of oscillatory and damping effects. This is based on joint work with A. Ionescu, B. Pausader and X. Wang.

Number Theory on 03 February 2025 at 15:00

Speaker: Tim Dokchitser (Bristol)
Title: TBA

Abstract: TBA

SBIDER on 03 February 2025 at 14:00

Speaker: Jessica Clark (University of Glasgow)
Title: Understanding mechanisms of inter-epidemic Rift Valley Fever virus transmission

Abstract: Rift Valley fever virus (RVF) is a zoonotic mosquito-borne virus. During outbreaks, infection causes devastating abortion storms in ruminant livestock. Historically, outbreaks have been observed to occur only every 5+ years after anomalous El Niño rains. Current control guidelines are tailored to this epidemiological pattern. However, recent serological evidence suggests ongoing inter-epidemic transmission in East Africa. We have developed mechanistic models to assess potential causes and implications of inter-epidemic transmission on control. We developed a network model with vector and host populations, and livestock movement informed by movement permit data from northern Tanzania to understand the conditions under which endemic transmission can be maintained in this region. Specifically, with this model we assess the sensitivity of the system to mosquito population dynamics, the role of livestock movement in maintaining onward transmission by connecting otherwise isolated metapopulations, and how existing immunity in a population due to inter-epidemic transmission, may shape transmission dynamics in the face of incursion.

Combinatorics on 31 January 2025 at 14:00

Speaker: Agelos Georgakopoulos (University of Warwick)
Title: A survey of coarse graph theory

Abstract: I will survey results and open questions on 'coarse graph theory', an emerging area that combines ideas from graph theory and coarse geometry.

Algebraic Geometry on 29 January 2025 at 16:00

Speaker: Taro Sano (Kobe University)
Title: Delta invariants of Fano weighted hypersurfaces

Abstract: K-stability (or existence of Kähler-Einstein metrics) of explicit Fano varieties has been studied for a long time. Delta invariants (stability thresholds) detect the K-stability of Fano varieties. Moreover, Abban--Zhuang developed a powerful method to compute the delta invariants by adjunctions. In this talk, I will explain our recent results on the K-stability of some Fano weighted hypersurfaces via the Abban--Zhuang method.

Algebraic Geometry on 29 January 2025 at 15:00

Speaker: Livia Campo (University of Vienna)
Title: K-stablity of Fano threefold hypersurfaces of index 1

Abstract: The existence of Kaehler-Einstein metrics on Fano 3-folds can be determined by studying lower bounds of stability thresholds. An effective way to verify such bounds is to construct flags of point-curve-surface inside the Fano 3-folds. This approach was initiated by Abban-Zhuang, and allows us to restrict the computation of bounds for stability thresholds only on flags. We employ this machinery to prove K-stability of terminal quasi-smooth Fano 3-fold hypersurfaces. This is deeply intertwined with the geometry of the hypersurfaces: in fact, birational rigidity and superrigidity play a crucial role. The superrigid case had been attacked by Kim-Okada-Won. In this talk I will discuss the K-stability of strictly rigid Fano hypersurfaces via Abban-Zhuang Theory. This is a joint work with Takuzo Okada.

Soft Matter Lunches on 29 January 2025 at 13:00

Speaker: Gareth Alexander (University of Warwick)
Title: Chiral active matter and odd mechanics

Abstract: I will describe my recent and ongoing research in chiral active matter in informal style. This is joint work with SJ Kole, Ananyo Maitra, Sriram Ramaswamy, and, separately, Sami Al-Izzi.

Algebraic Topology on 28 January 2025 at 16:00

Speaker: Paul Balmer (UCLA)
Title: Completion in tensor-triangular geometry

Abstract: We'll review the notion of completion, à la Bousfield, and discuss its significance in tensor-triangular geometry. The problem appears in the very fundamental situation where one tries to patch the spectrum together from a partition consisting of an open and its closed complement. We shall also discuss examples, in commutative algebra and in representation theory of finite groups.

Number Theory on 27 January 2025 at 15:00

Speaker: Abhishek Saha (QMUL)
Title: Holomorphic QUE for Siegel cusp forms: the case of Saito-Kurokawa lifts

Abstract: The Quantum Unique Ergodicity (QUE) conjecture was proved in the classical case of Maass forms on the upper-half plane by Lindenstrauss and Soundararajan. The analogous mass equidistribution statement for holomorphic cusp forms in the weight aspect is a theorem due to Holowinsky and Soundararajan. In this talk, I will discuss some recent joint work with Jesse Jaasaari and Steve Lester on the higher rank analogue of the result of Holowinsky and Soundararajan for the case of holomorphic Siegel cusp forms. Our main result establishes mass equidistribution for Saito-Kurokawa lifts (which are special types of Siegel cusp forms of degree 2) assuming the Generalized Riemann Hypothesis (GRH) . We also show that this implies the equidistribution of zero divisors of Saito-Kurokawa lifts. Time permitting, I will say a few words about generalisation to higher dimensions.

DAGGER on 27 January 2025 at 14:00

Speaker: Mats Bylund (Université Paris-Saclay)
Title: Collet-Eckmann and hyperbolicity in unicritical dynamics

Abstract: The Collet-Eckmann condition plays an important role in the study of both real and rational dynamics. This condition, which requires exponential increase of the derivative along the critical orbit(s), is known to be abundant in the real quadratic setting, and also in the rational setting. For complex quadratic maps, the set of Collet-Eckmann parameter are known to constitute a set of zero Lebesgue measure (area), but full harmonic measure. An important open question in complex dynamics is the Fatou conjecture: Does the set of hyperbolic complex quadratic maps constitute a dense set? In this talk I will discuss this question in a strong form around Collet-Eckmann parameters: Every unicritical Collet-Eckmann parameter is a Lebesgue density point of the complement of the Mandelbrot set. This talk is based on joint work with Magnus Aspenberg and Weiwei Cui.

SBIDER on 27 January 2025 at 14:00

Speaker: Edward Offord (University of Warwick)
Title: Single cell time series analysis using graph neural networks

Abstract: The analysis of individual biological cells is important to understand how many processes in the human body function. Software is required to parse the large volumes of data collected. Graph neural networks offer a generalized method for extracting useful information from time-series data. As an example, Dictyostelium preforming 'cell drinking' (shared by many human cancer cells) is used to demonstrate the potential of these networks to aid in our understanding of subcellular processes. 'Cell drinking' is characterized by an invagination that develops on the surface of the cell; here the graph neural network detects and extracts a complete life cycle of the surface deformation. The invaginations (called macropinocytic cups) then provide insight into how the surface deformation is formed over time. Understanding the mechanism in greater detail enables researchers to experiment with the development of drugs that can either excite or inhibit the formations of these structures.

Colloquium on 24 January 2025 at 16:00

Speaker: Max Stolarski (Warwick)
Title: Singularity Analysis of Geometric Flows

Abstract: Geometric flows, like the mean curvature flow and Ricci flow, prescribe the time evolution of some geometric object according to its geometry. These flows have found applications in geometry and topology as well as mathematical models of physical systems that include moving boundaries. Due to nonlinear effects, geometric flows often form singularities in finite time. Analysis of these singularities is then essential for applications. We'll discuss geometric flow singularities where the evolving manifold looks like a cone near the singularity. These conical singularities give a rich source of examples of interesting dynamics, including bounded curvature quantities near singularities and non-unique continuations through singularities. We'll explore developments here and discuss implications for the general dynamics of weak geometric flow solutions.

Combinatorics on 24 January 2025 at 14:00

Speaker: Bobby Miraftab (Carleton University)
Title: Infinite Cycles in Cayley Graphs and Eigenvectors of Finite Support

Abstract: This talk has two parts. In the first part, we explore infinite cycles in Cayley graphs. A weaker version of the celebrated Lovász conjecture asserts that every finite, connected Cayley graph contains a hamiltonian cycle. While infinite graphs cannot possess hamiltonian cycles in the traditional sense, there are natural analogues. We focus on a topological approach to this problem, demonstrating how some results for finite Cayley graphs can be extended to the infinite case. Additionally, we propose some open questions. In the second part, we turn our attention to constructions of locally finite graphs with eigenvectors of finite support, particularly for "very symmetric" graphs and over finite fields. We will provide some background, present basic constructions yielding "somewhat symmetric" examples, and discuss obstructions that preclude certain potential examples.

Mathematics Teaching and Learning on 23 January 2025 at 16:00

Speaker: Maria-Louiza Van Den Bergh (Warwick Statistics)
Title: Improving Reliability in Comparative Judgement: Using Bootstrapping and Alternate Strength Parameter

Abstract: Comparative Judgement is an assessment method by which item ratings are estimated based on rankings of subsets of the items. To be able to use this as an alternative assessment technique, it is important to establish the credibility of the ratings produced. This presentation discusses the shortcomings of the popular SSR method and explores using bootstrapping and an alternative strength parameter as a more effective method.

Analysis on 23 January 2025 at 16:00

Speaker: Francesca Tripaldi (Leeds)
Title: Extracting subcomplexes in the subRiemannian setting

Abstract: On subRiemannian manifolds, the de Rham complex is not the ideal candidate to use to carry out geometric analysis. However, special subcomplexes have successfully been applied in very specific settings, such as Heisenberg groups and the Cartan group. I will give an overview of different techniques used to obtain such subcomplexes, as well as point out their limitations when used on arbitrary Carnot groups, and a possible way to overcome them.

Algebraic Geometry on 22 January 2025 at 15:00

Speaker: Elena Maria Guardo (Università di Catania)
Title: Expecting unexpected hypersurfaces

Abstract: Let X be a reduced subscheme in Pn. We say that X admits an unexpected hypersurface of degree d and multiplicity m if the imposition of having multiplicity m at a general point P fails to impose the expected number of conditions on the linear system of hypersurfaces of degree d containing X. We introduce new methods for studying unexpectedness, such as the use of generic initial ideals and partial elimination ideals to clarify when it can and when it cannot occur. We formulate a new way of quantifying unexpectedness (our AV sequence), which allows us detect the extent to which unexpectedness persists as increases but remains constant. We also study how knowledge of the Hilbert function, together with certain geometric assumptions, can provide information about unexpected hypersurfaces. This is based on the joint paper with G. Favacchio, B, Harbourne, and J. Milgliore.

Algebraic Topology on 21 January 2025 at 16:00

Speaker: Sofia Marlasca Aparicio (Oxford)
Title: Ultrasolid Geometry and Deformation Theory

Abstract: We will introduce ultrasolid modules, a variant of the solid modules of Clausen and Scholze, which generalise complete modules over a field k. In this setting, we show some commutative algebra results like an ultrasolid variant of Nakayama's lemma. We also explore higher algebra in the form of animated and E∞ ultrasolid k-algebras. Finally, we will apply this to generalise the Lurie-Schlessinger criterion in deformation theory (no previous knowledge of deformation theory is assumed).

PDE and Analysis Seminar (joint) on 21 January 2025 at 12:00

Speaker: Antonín Češík (University of Warwick)
Title: Variational methods for dynamical PDE: visco-elastic solids with collisions and fluid-structure interactions.

Abstract: Energy-based methods have often proven useful in analysis of evolutionary PDEs. They open the problems to powerful analytical tools from calculus of variations. In particular the celebrated De Giorgi's minimizing movements method, which can handle gradient flows and quasi-static problems. A recently developed "hyperbolic minimizing movements" method extends this to the case of fully dynamical problems (i.e. including inertia). It combines the variational approach to handle nonlinearities, and PDE estimates to handle the kinetic energy. In this talk, we present some recent applications of this to applications to fully dynamical problems. First, we obtain the existence result for nonlinear viscoelastic solids in the large deformation regime with arbitrary collisions. For this we construct a physically correct measure-valued contact force. Next, we treat nonlinear viscoelastic bulk solid coupled to a Navier-Stokes equation with a full slip condition at the fluid-solid interface. We complement these results by studying the fully time-discrete version of the scheme, as a step towards future numerical implementations. The talk is based on joint works with G. Gravina, M. Kampschulte, S. Schwarzacher.

Number Theory on 20 January 2025 at 15:00

Speaker: Robin Bartlett (Glasgow)
Title: TBA

Abstract: TBA

SBIDER on 20 January 2025 at 14:00

Speaker: Valaire Yatat (University of Yaounde 1, Cameroon)
Title: Modelling the Impact of the Sterile insect technique with accidental releases of sterile females on mosquito-borne diseases control when viruses are circulating

Abstract: The sterile insect technique (SIT) is a technique to control some vectors of diseases by releasing sterile males. However, during these releases, sterilized females can be (accidentally) released and since only females are vectors of diseases, it is important to study their impact when arthropod viruses are circulating. To that aim, we develop and study an entomological-epidemiological model, considering either permanent or periodic releases. Our results reveal that outside an epidemic period, the release of sterile females is not an issue, as long as the sterile males release rate is greater than $\Lambda_M^{crit}$}. Within an epidemic period, we show that sterile females releases do not really impact the SIT efficiency, as long as the release rate, $\Lambda_F$, is lower than a critical value, $\Lambda_F^{crit}$, that depends on the mosquito and epidemiological threshold parameters, $\N$, and $\R_0^2$. To illustrate numerically our theoretical results, we consider Dengue parameters. We estimate all thresholds and also the effective reproduction number, $\R_{eff}^2$, and highlight the importance of early permanent or periodic SIT control to prevent or mitigate the risk of a Dengue epidemic, with and without sterile female releases.

Combinatorics on 17 January 2025 at 14:00

Speaker: Julian Sahasrabudhe (University of Cambridge)
Title: A new lower bound for sphere packing

Abstract: What is the maximum proportion of d-dimensional space that can be covered by disjoint, identical spheres? In this talk I will discuss a new lower bound for this problem, which is the first asymptotically growing improvement to Rogers' bound from 1947. Our proof is almost entirely combinatorial and reduces to a novel theorem about independent sets in graphs with bounded degrees and codegrees. This is based on joint work with Marcelo Campos, Matthew Jenssen and Marcus Michelen.

Analysis on 16 January 2025 at 16:00

Speaker: Nicola Gigli (SISSA)
Title: Trading linearity for ellipticity - a novel approach to global Lorentzian geometry

Abstract: The concepts of Sobolev functions, elliptic operators and Banach spaces are central in modern geometric analysis. In the setting of Lorentzian geometry, however, unless one restricts the attention to Cauchy hypersurfaces these do not have a clear analogue, due to the signature of the metric tensor. Aim of the talk is to discuss some recent observations in this direction centered around the fact that for $p<1$ the $p$-D’Alambertian is elliptic on the space of time functions. The talk is mostly based on joint project with Beran, Braun, Calisti, McCann, Ohanyan, Rott, Saemann.

Mathematics Teaching and Learning on 16 January 2025 at 16:00

Speaker: Wodu Majin (Sheffield Hallam)
Title: Helping students develop a richer understanding of mathematics: a case study of mind maps

Abstract: I will discuss how I have used mind maps in my teaching. In particular, I will describe an assignment in which students were asked to produce mind maps in a module that heavily featured numerical methods. I will explain my reasons for developing this kind of assignment and what skills I wanted students to develop. I will also reflect on the implementation of the assignment, and on student engagement with it. I will use this as a springboard to briefly discuss challenges and possibilities of helping students develop a richer understanding of mathematics.

Algebraic Geometry on 15 January 2025 at 15:00

Speaker: Miles Reid (Warwick)
Title: The Tate-Oort group TO_n for n >= 1

Abstract: The cyclic group Z/n as you have never seen it before.

Number Theory on 13 January 2025 at 15:00

Speaker: Max Xu (Simons/Courant Institute)
Title: Nonnegative partial sums of quadratic characters

Abstract: In 1911, Fekete proposed the problem of studying how likely a Fekete polynomial has no real zeros in [0,1]. A related question by Polya is to ask how likely a random quadratic character always has nonnegative partial sums. Notably, the work of Baker and Montgomery in 1989 qualitatively showed both events are rare, in the sense that the asymptotic density is zero. In a joint work in progress with Angelo and Soundararajan, we give a quantitative upper bound which is (we believe) close to the truth, and in fact we believe there are plenty of such polynomials and characters.

Colloquium on 10 January 2025 at 16:00

Speaker: Jerome Neufeld (Cambridge)
Title: Flow and flexure: Subglacial hydrology and the transient response of ice sheets

Abstract: The response of the Greenland and Antarctic ice sheets to a changing climate is one of the largest sources of uncertainty in future sea level predictions. The behaviour of the subglacial environment, where ice meets hard rock or soft sediment, is a key determinant in the flux of ice towards the ocean, and hence the loss of ice over time. Predicting how ice sheets respond on a range of timescales brings together mathematical models of the elastic and viscous response of the ice, subglacial sediment and water and is a rich playground where the simplified models of the contact between ice, rock and ocean can shed light on very large scale questions. In this talk we’ll see how these simplified models can make sense of a variety of field and laboratory data in order to understand the dynamical phenomena controlling the transient response of large ice sheets.

Analysis on 09 January 2025 at 16:00

Speaker: Arjun Sobnack (Warwick)
Title: Delayed parabolic regularity for the Curve Shortening Flow

Abstract: The Curve Shortening Flow (CSF) is a parabolic partial differential equation (PDE) which arises as the L^2–gradient flow of the length functional. It is a general phenomenon that parabolic PDEs do not observe an instantaneous L^1–smoothing property (as they do for L^{1 Nevertheless, in a recent preprint P. M. Topping & S. propose the framework that, two planer curves evolving under the CSF to trap a fixed area start observing a smoothing estimate after waiting for a time depending only on the area, which is a type delayed L^1-smoothing estimate. The aim of this talk is to introduce the principle of delayed parabolic regularity for the CSF and to demonstrate that it is sharp, and also to present some applications of localised versions of the estimates.

Mathematics Teaching and Learning on 08 January 2025 at 14:00

Speaker: Claire Milburn and Howard Fooksman (Turnitin)
Title: Gradescope

Abstract: This presentation will show how Gradescope can hugely improve the efficiency of assignment and exam marking. Trusted by Leeds, LSE, KCL, Durham, Reading and many other universities, Gradescope helps instructors grade assessments in a fraction of the time compared with traditional pen-and-paper marking. Gradescope also offers support for multiple markers, detailed feedback to students, and rubric-based marking for improved consistency. The demo will be followed by a Q&A session where we will be joined by Prof. Iñaki García Etxebarria (Durham) who will share his experience of using Gradescope at Durham maths department.

Number Theory on 06 January 2025 at 15:00

Speaker: Sean Eberhard (Warwick)
Title: TBA

Abstract: TBA

MIR@W on 09 December 2024 at 16:00

Speaker: Draga Pihler-Puzović (University of Manchester)
Title: Modelling hydrogels: building networks in the Mathematical Sciences [MIRaW day]

Abstract: TBA

MIR@W on 09 December 2024 at 14:30

Speaker: Chris MacMinn (University of Oxford)
Title: Modelling hydrogels: building networks in the Mathematical Sciences [MIRaW day]

Abstract: TBA

MIR@W on 09 December 2024 at 13:30

Speaker: Matt Butler, Joseph Webber, Callum Cuttle (University College London, University of Warwick, University of Oxford)
Title: ECR Talks - Modelling hydrogels: building networks in the Mathematical Sciences [MIRaW day]

Abstract: TBA

MIR@W on 09 December 2024 at 11:45

Speaker: Matt Hennessy (University of Bristol)
Title: Modelling hydrogels: building networks in the Mathematical Sciences [MIRaW day]

Abstract: TBA

MIR@W on 09 December 2024 at 11:00

Speaker: Grae Worster (University of Cambridge)
Title: Modelling hydrogels: building networks in the Mathematical Sciences [MIRaW day]

Abstract: TBA

MIR@W on 09 December 2024 at 10:30

Speaker: Philip Pearce (University College London)
Title: Modelling hydrogels: building networks in the Mathematical Sciences [MIRaW day]

Abstract: TBA

Colloquium on 06 December 2024 at 16:00

Speaker: Silke Weinfurtner (Nottingham)
Title: Exploring Classical and Quantum Fields in Curved Spacetimes: Lab-Based Investigations into Black Holes and Early Universe Physics

Abstract: Exploring the dynamics of the early universe and black holes unveils profound insights into the interplay between general relativity and classical/quantum fields. Important phenomena emerge when gravitational and/or field interactions are strong, and/or when quantum effects become prominent. Notable examples include Hawking's proposal on the evaporation of black holes, Penrose's conjecture on the spin-down of rotating black holes, and Kofman's proposal on particle production during preheating. Despite their significance, observing these phenomena directly remains elusive. In this presentation, I will report on recent advancements in investigating these processes in laboratory experiments involving normal and quantum liquids.

Combinatorics on 06 December 2024 at 14:00

Speaker: Debmalya Bandyopadhyay (University of Birmingham)
Title: Monochromatic tight cycle partitions in edge-coloured complete $k$-graphs

Abstract: Let $K_n^{(k)}$ be the complete $k$-uniform hypergraph on $n$ vertices. A tight cycle is a $k$-uniform graph with its vertices cyclically ordered so that every~$k$ consecutive vertices form an edge, and any two consecutive edges share exactly~$k-1$ vertices. A result by Bustamante, Corsten, Frankl, Pokrovskiy and Skokan shows that all $r$-edge coloured $K_{n}^{(k)}$ can be partition into $c_{r,k}$ vertex disjoint monochromatic tight cycles. However, the constant $c_{r,k}$ is of tower-type. In this work, we show that $c_{r,k}$ is a polynomial in~$r$.

Analysis on 05 December 2024 at 16:00

Speaker: Michele Villa (EHU Bilbao)
Title: Uniform rectifiability and Poincaré inequalities

Abstract: Some years ago, J. Azzam showed that any d-Ahlfors regular subset of the n-Euclidean space supporting a weak (1,d)-Poincaré inequality with respect to surface measure is uniformly rectifiable. This talk, based on a work (in progress!) with M. Hyde and I. Violo, concerns itself with the converse statement: that any d-uniformly rectifiable set is contained in a set supporting a weak Poincaré inequality. If time permits, I will outline some parts of the construction, and remarks on some future research directions.

Geometry and Topology on 05 December 2024 at 13:30

Speaker: Peter Patzt (University of Oklahoma)
Title: Unstable cohomology of SL_n Z and Hopf algebras

Abstract: The cohomology of SL_n Z has many connections to geometry and number theory and is largely unknown. In this talk, I will give a survey about what is known about it. In particular, I will include newly found unstable classes which come from a Hopf algebra structure. This talk is on joint work with Avner Ash and Jeremy Miller.

Algebra on 05 December 2024 at 12:00

Speaker: Patricia Medina Capilla (Warwick)
Title: The second maximal subgroups of the almost simple groups

Abstract: In 2018, Lucchini, Marion, and Tracey showed that every maximal subgroup of an almost simple group is 5-generated, lowering the previously known bound of 6. Naturally, one can ask the same about second maximal subgroups of almost simple groups. Burness, Liebeck and Shalev looked into this question in 2016, determining that almost all such subgroups were 70-generated. In this talk, we will present recent work aiming to lower this bound, and survey some of the key techniques involved. In particular, we will discuss the method of crowns, developed by Lucchini and Dalla Volta and used by Lucchini, Marion and Tracey to great effect, as well as an improved classification of the second maximal subgroups of almost simple groups with alternating or classical socle.

Algebraic Topology on 03 December 2024 at 17:00

Speaker: Irakli Patchkoria (University of Aberdeen)
Title: On the Farrell-Tate K-theory of Out(F_n)

Abstract: This is joint work with Naomi Andrew. The classical Farrell-Tate cohomology measures the failure of duality in group (co)homology. Brown in 70s gave a general method for computing the p-local part of the Farrell-Tate cohomology. Using Brown’s methods Farrell-Tate cohomology has been computed for various arithmetic groups, mapping class groups and Out(F_n)-s, outer automorphism groups of Free groups. Later Klein introduced generalised Farrell-Tate cohomology with coefficients in an arbitrary spectrum. In this project we investigate the Farrell-Tate K-theory of Out(F_n). We will show that for any discrete group with finite classifying space for proper actions, the p-adic Farrell-Tate K-theory is rational. Then using Lück’s Chern character, we will give a general formula for the p-adic Farrell-Tate K-theory in terms of centralisers. In particular, we apply this formula to Out(F_{p+1}) which has curious p-torsion behaviour: It has exactly one conjugacy class of a p-torsion element which does not come from Aut(F_{p+1}). Computing the rational cohomology of the centraliser of this element allows us to fully compute the p-adic Farrell-Tate K-theory of Out(F_{p+1}). As a consequence we show for example that the 11-adic Farrell-Tate K-theory of Out(F_{12}) is non-trivial, thus detecting a non-trivial class in odd K-theory of Out(F_{12}) without using any computer calculations.

Partial Differential Equations and their Applications on 03 December 2024 at 12:00

Speaker: Amirali Hannani (KU Leuven)
Title: TBA

Abstract: TBA

Number Theory on 02 December 2024 at 15:00

Speaker: Nikolaos Diamantis (Nottingham)
Title: L-series of half-integral weight cusp forms and an analogue of the period polynomial

Abstract: We construct a polynomial expressed in terms of values of the L-series attached to a half-integral weight cusp form. This polynomial can be thought of as an analogue of the classical period polynomial since it also satisfies certain "period relations". We show how it induces a lift of half-integral weight cusp forms to integral weight forms which is compatible with the L-series of the respective forms. This lift is explicit thanks to a result by Pasol and Popa. (Joint work with Branch, Raji and Rolen).

DAGGER on 02 December 2024 at 14:00

Speaker: Leon Starešinić (Imperial College London)
Title: Density of Stable Interval Translation Maps

Abstract: Interval Translations Maps (ITM’s) are a natural generalisation of the well-known Interval Exchange Transformations (IET’s). They are obtained by dropping the bijectivity assumption for IET’s. As such they are exactly the finite piece-wise isometries of the interval. There are two types of ITM’s, finite-type and infinite-type ones. They are classified by their non-wandering sets: it is a finite union of intervals for finite-type maps, and contains a Cantor set for infinite-type maps. One of the basic questions in the field is: How prevalent is each type of map in the parameter space? In this work, we show that the stable maps form a dense set in the parameter space of ITM’s with a fixed number of intervals, thus showing the prevalence of finite type maps in the topological sense. The key ingredient of this work is a theorem about linear independence of certain critical itinerary vectors.

SBIDER seminar on 02 December 2024 at 14:00

Speaker: Nardus Mollentze (University of Glasgow)
Title: Predicting spatial expansions in the risk of virus spillover from vampire bats

Abstract: Common vampire bats are distributed throughout much of Latin America, where their obligate blood feeding lifestyle creates a high risk for cross-species transmission of viruses to humans and livestock. While it remains difficult to study virus transmission directly in the bat population, thousands of spillovers of rabies virus to livestock reveals distinctive signatures of both endemic circulation and epidemic spread in the reservoir. I will discuss recent work combining Bayesian phylogeography and fine-scale mixture models of the rate and probability of invasions to examine the factors predicting spatial expansions in the areas experiencing spillovers. I will also briefly describe the ongoing development of a massively multiplexed serology assay which which will allow us to directly track the circulation of all known bat-associated viruses. By improving our understanding of the spatial spread of viruses in this key reservoir, these studies are bringing us closer to the long-awaited goal of predicting spillover risk in space and time.

Combinatorics on 29 November 2024 at 14:00

Speaker: Peleg Michaeli (University of Oxford)
Title: Extremal and probabilistic aspects of graph rigidity

Abstract: Combinatorial rigidity theory addresses questions such as: given a structure defined by geometric constraints, what can be inferred about its geometric behaviour based solely on its underlying combinatorial data? Such structures are often modelled as assemblies of rigid rods connected by rotational joints, in which case the underlying combinatorial data is a graph. A typical question in this context is: given such a framework in generic position in R^d, is it rigid? That is, does every continuous motion of the vertices (joints) that preserves the lengths of all edges (rods) necessarily preserve the distances between all pairs of vertices? In this talk, I will present new sufficient conditions for the rigidity of a framework in R^d based on the notion of rigid partitions - partitions of the underlying graph that satisfy certain connectivity properties. I will outline several broadly applicable conditions for the existence of such partitions and discuss a few applications, among which are new results on the rigidity of highly connected and (pseudo)random graphs. If time allows, I will also discuss new - often sharp - sufficient minimum degree conditions for d-dimensional rigidity and mention a related novel result on the pseudoachromatic number of graphs. The talk is based on joint works with Michael Krivelevich and Alan Lew.

Analysis on 28 November 2024 at 16:00

Speaker: Luca Gennaioli (Warwick)
Title: On the Fourier transform of BV functions

Abstract: In this talk we shall investigate the relation between the Fourier transform of ${\rm BV}$ (bounded variation) functions and their singularities. We will discuss some averaged Plancherel identities for ${\rm BV}$ functions and a new characterisation of sets of finite perimeter in terms of their Fourier transform.

Geometry and Topology on 28 November 2024 at 13:30

Speaker: Simon Machado (ETH Zurich)
Title: Approximate lattices: structure and beyond

Abstract: Approximate lattices are aperiodic generalisations of lattices in locally compact groups. Yves Meyer first introduced them in abelian groups before studying them as mathematical models for quasi-crystals. Since then, their structure has been thoroughly investigated in both abelian and non-abelian settings. The primary motivation behind this research was to extend Meyer’s foundational theorem to non-abelian locally compact groups. This generalisation has now been established, and I will discuss the resulting structure theory. I will highlight certain concepts, including a notion of cohomology that lies between group cohomology and bounded cohomology, which plays a significant role in their study. Additionally, I will formulate open problems and conjectures related to approximate lattices.

Algebraic Geometry on 27 November 2024 at 13:00

Speaker: Elena Denisova (University of Edinburgh)
Title: Delta-invariants of Du Val del Pezzo surfaces

Abstract: It is known that a Fano variety with “mild” singularities admits a Kahler Einstein metric if and only if it is K-polystable. For two-dimensional Fano varieties (del Pezzo surfaces) Tian and Yau proved that a smooth del Pezzo surface is K-polystable if and only if it is not a blow up of P2 in one or two points. A lot of research was done for threefolds however, not everything is known and often the problem can be reduced to computing δ-invariant of (possibly singular) del Pezzo surfaces. In my talk I will describe the status of the problem, present an example of computation of δ-invariant, show the example of application of this result for a singular Fano threefold and explain a possible direction for future research.

Algebraic Topology on 26 November 2024 at 17:00

Speaker: Markus Hausmann (University of Bonn)
Title: The universal property of bordism rings of manifolds with commuting involutions

Abstract: My talk concerns bordism rings of compact smooth manifolds equipped with a smooth action by a finite group. I will start by recalling classical results on the subject from the 60's and 70's, mostly due to Conner-Floyd, Boardman, Stong and Alexander. Afterwards I will discuss joint work with Stefan Schwede in which we prove an algebraic universal property for the collection of bordism rings of manifolds with commuting involutions, in the representation-graded sense. This universal property can be viewed as a delocalization of the corresponding one for homotopical equivariant bordism rings.

Partial Differential Equations and their Applications on 26 November 2024 at 12:00

Speaker: Noemi David (Rouen)
Title: TBA

Abstract: TBA

Number Theory on 25 November 2024 at 15:00

Speaker: Elvira Lupoian (Imperial)
Title: Runge’s Method and Integral Points on Modular Curves

Abstract: The study of integral points on curves dates to Siegel’s theorem in 1929, which has been historically studied by many due to its connections to Mordell’s conjecture (Faltings’ theorem) . More recently, Bilu and Parent were able to prove Serre’s uniformity conjecture in the split Cartan case by studying integral points on the corresponding modular curve. Their proof relies on efficiently determining the integral points using the so -called Runge’s method. In this talk, we review this method and discuss how the work of Bilu and Parent can be adapted to efficiently bounds heights of integral points on certain covers of the classical modular curve $X_{0} \left( p \right)$.

DAGGER on 25 November 2024 at 14:00

Speaker: Gabriel Corrigan (University of Glasgow)
Title: Realising virtual cohomological dimension of automorphism groups of RAAGs

Abstract: In 1986, Culler & Vogtmann introduced 'Outer space' - a complex upon which Out(F_n), the outer automorphism group of a free group, acts properly. This had many applications; one is that the dimension of the so-called 'spine' of Outer space is precisely the virtual cohomological dimension (VCD) of Out(F_n). More recently, Charney-Stambaugh-Vogtmann constructed an 'untwisted Outer space' - an analogous space used for studying the group of untwisted automorphisms of a right-angled Artin group. However, in a departure from the free group case, sometimes the dimension of this rather natural 'untwisted spine' is larger than the VCD of the corresponding group of outer automorphisms! In this talk I will present work examining this phenomenon. I give graph-theoretic conditions under which we can perform an equivariant deformation retraction of the untwisted spine to produce a new complex which geometrically realises the VCD of the group of untwisted automorphisms. As a corollary, this proves that the gap between the VCD of the untwisted subgroup and the dimension of the untwisted spine can be arbitrarily large.

SBIDER on 25 November 2024 at 14:00

Speaker: Caroline Trotter (University of Cambridge)
Title: Defeating Meningitis by 2030: how can modelling help?

Abstract: The World Health Organisation has developed an ambitious roadmap to Defeat Meningitis by 2030. The use of vaccines is key to reducing the burden of disease due to meningitis, particularly the most common forms of bacterial meningitis. A key goal is to eliminate epidemics of meningitis, which occur periodically but irregularly, in the African meningitis belt. I will describe how modelling can be used in support of the roadmap, particularly in providing evidence for vaccine policy and epidemic response.

Combinatorics on 22 November 2024 at 14:00

Speaker: Maria Ivan (University of Cambridge)
Title: Euclidean Ramsey sets and the block sets conjecture

Abstract: A set $X$ is called Euclidean Ramsey if, for any $k$ and sufficiently large $m$, any $k$-colouring of $\mathbb{R}^m$ contains a monochromatic congruent copy of $X$. This notion was introduced by Erd\H{o}s, Graham, Montgomery, Rothschild, Spencer and Straus. They asked if a set is Ramsey if and only if it is spherical, meaning that it lies on the surface of a sphere. It is not too difficult to show that if a set is not spherical, then it is not Euclidean Ramsey either, but the converse is very much open despite extensive research over the years. On the other hand, the block sets conjecture is a purely combinatorial, Hales-Jewett type of statement. It was introduced in 2010 by Leader, Russell and Walters. If true, the block sets conjecture would imply that every transitive set (a set whose symmetry group acts transitively) is Euclidean Ramsey. Similarly to the first question, the block sets conjecture remains very elusive. In this talk we discuss recent developments on the block sets conjecture and their implications to Euclidean Ramsey sets. Joint work with Imre Leader and Mark Walters.

Analysis on 21 November 2024 at 16:00

Speaker: Guido De Philippis (NYU)
Title: Decay of excess for the abelian Higgs model

Abstract: Entire critical points of the Yang–Mills–Higgs functional are known to blow down to (generalized) minimal surfaces. Goal of the talk is to prove an Allard's type large scale regularity result for the zero set of the solution. In particular, in the "multiplicity one" energy regime, we show uniqueness blow-downs and we classify entire solutions in small dimensions and of entire minimizers in any dimension. This is based on a joint work with Aria Halavati and Alessandro Pigati.

Statistical Mechanics on 21 November 2024 at 14:00

Speaker: Harini Desiraju (University of Sydney)
Title: Probabilistic conformal blocks on the torus and the Lamé equation

Abstract: Conformal blocks are the fundamental building blocks of Conformal Field Theories and play an important role in several areas of mathematical physics from random geometry to black hole physics. Starting from their probabilistic formulation in terms of the Gaussian Multiplicative Chaos (GMC) measure by Promit Ghosal, Guillaume Remy, Xin Sun, Yi Sun, I will prove certain conjectures posed by Zamolodchikov regarding the semiclassical behaviour of conformal blocks and show their relation to the Lamé equation, and other associated integrable structures. This talk is based on a joint work with Promit Ghosal and Andrei Prokhorov (arXiv: 2407.05839).

Geometry and Topology on 21 November 2024 at 13:30

Speaker: Harry Petyt (University of Oxford)
Title: Obstructions to cubulation

Abstract: One can get a lot of information about a group by getting it to act geometrically on a CAT(0) cube complex. When this is possible there is a standard framework for trying to find the action, known as Sageev's construction. On the other hand, whilst most groups will not admit such actions, there is a real lack of ways to actually rule out the possibility that they exist. This talk will discuss joint work with Zach Munro, where we give a geometric obstruction to the possibility of cubulating groups.

Algebra on 21 November 2024 at 12:00

Speaker: Luca Sabatini (Warwick)
Title: Abelian subgroups and sections of finite groups

Abstract: Let G be a group of order n, where n is a large integer. In 1976, Erdős and Straus used a simple argument to show that G contains an abelian subgroup of order roughly log n. Twenty years later, Pyber used the classification of the finite simple groups to improve this result up to 2^{\sqrt{\log n}}. This is best possible, because of certain wild p-groups of class 2 that were obtained with probabilistic methods by Ol'shanskii. On the other hand, it can be seen that G always contains an abelian section of size at least n^{1/ log log n}, which is much bigger. In this talk, we present these questions and some of the methods used in the proofs. We also introduce new probabilistic constructions of wild p-groups, which is joint work with S. Eberhard.

Algebraic Geometry on 20 November 2024 at 15:00

Speaker: Alapan Muckhopadyay (EPFL)
Title: Generators of bounded derived categories using the Frobenius map.

Abstract: Since the appearance of Bondal- van den Bergh’s work on the representability of functors, proving existence of strong generators of the bounded derived category of coherent sheaves on a scheme has been a central problem. While for a quasi-excellent, separated scheme the existence of strong generators is established, explicit examples of such generators are not common. In this talk, we show that explicit generators can be produced in prime characteristics using the Frobenius pushforward functor. As a consequence, for affine schemes, we show that the pushforward of the structure sheaf via a high enough iterate of the Frobenius is a generator. This recovers Kunz’s characterization of regularity using Frobenius. We will discuss examples indicating that in contrast to the affine situation, for a smooth projective scheme whether some Frobenius pushforward of the structure sheaf is a generator, depends on the geometry of the underlying scheme. Part of the talk is based on a joint work with Matthew Ballard, Srikanth Iyengar, Patrick Lank and Josh Pollitz.

Soft Matter Lunches on 20 November 2024 at 13:00

Speaker: Thomasina Ball, Danny Booth, Ellen Jolley, Ellen Luckins, Joe Webber (University of Warwick)
Title: APS DFD practice talks

Abstract: Thomasina Ball: Unravelling wrinkle formation in a lubricated viscoplastic beam (60 second flashtalk) Danny Booth: Bubble racing in a Hele-Shaw cell (60 second flashtalk) Ellen Jolley: Translation of a viscoelastic cell surrounded by a Newtonian fluid (10 minute talk) Ellen Luckins: Modelling evaporation-driven flows in capillary porous media (60 second flashtalk) Joe Webber: XOXO, Gossip Gel: oscillating chemical reactions facilitate communication between responsive hydrogels (10 minute talk)

Algebraic Topology on 19 November 2024 at 17:00

Speaker: Martin Gallauer (Warwick)
Title: Derived commutative algebraic geometry

Abstract: Venerable algebraic geometry (AG) has many descendants, including relatively recently "derived noncommutative AG" (Kapranov, Bondal, Orlov, Kontsevich,...). In this expository talk I will discuss an even younger one that one might call "derived commutative AG" and which Balmer introduced as "tensor-triangular geometry". Comparing the main features I'll try to pitch it as an attractive addition to the family.

Partial Differential Equations and their Applications on 19 November 2024 at 12:00

Speaker: Jakub Skrzeczkowski (Oxford)
Title: TBA

Abstract: TBA

Number Theory on 18 November 2024 at 15:00

Speaker: Emma Bailey (Bristol)
Title: Large deviations of Selberg’s CLT: upper and lower bounds

Abstract: Selberg’s CLT informs us that the logarithm of the Riemann zeta function evaluated on the critical line behaves as a complex Gaussian. It is natural, therefore, to study how far this Gaussianity persists. This talk will present conditional and unconditional results on atypically large values, and is joint with Louis-Pierre Arguin and Asher Roberts.

DAGGER on 18 November 2024 at 14:00

Speaker: Anna Jové (Universitat de Barcelona)
Title: What is a Baker domain? Introduction to transcendental dynamics

Abstract: Transcendental dynamics, in contrast with rational dynamics, present richer structures, even in the Fatou set, motivated by the presence of an essential singularity and the infinite degree of the iterated map. Essentially, such structures are wandering domains and Baker domains. In this talk, first I will present the definition of Baker domain and their classification, and then we will shift to their boundary dynamics, which is essentially chaotic, and a great source of open questions. Some conjectures and open problems will be presented, together with some new results, which are joint work with N. Fagella.

SBIDER on 18 November 2024 at 14:00

Speaker: Weini Huang (Queen Mary University)
Title: Mathematical models of extra-chromosomal DNA and their applications in cancer

Abstract: Many diseases in human including cancers are caused by genetic alternations/errors starting from a single cell. The origin of these genetic errors and the expansion of the abnormal cells carrying these genetic errors are often stochastic processes. Here we develop a general framework to model the dynamics of cancer cells carrying extra-chromosomal DNA (ecDNA), a genetic error found in more than 30% of tumour samples across various cancer types and correlated to the worse clinical outcomes. Different from chromosomal DNA where genetic materials are on average equally divided to daughter cells controlled by centromeres during mitosis, the segregation of ecDNA copies is random partition and leads to a fast accumulation of cell-to-cell heterogeneity in copy numbers. We use deterministic and stochastic approaches to analyse the fraction of cells carrying ecDNA and copy number distributions, and use those distributions observed in experimental and clinical data to infer the selection strength of ecDNA positive cells. We further extend our model of a single ecDNA species where all ecDNA copies are identical in genetic structure and function, to multiple ecDNA types where ecDNA copies can have different genes (species), mutations (genotypes), or have different functions without genetic changes (phenotypes). All these variations of our basic model can be applied to relevant biological context and provide insight to understand ecDNA dynamics observed in clinic or experiments and improve treatment strategies.

Combinatorics on 15 November 2024 at 14:00

Speaker: Brett Kolesnik (University of Warwick)
Title: Graphical sequences and plane trees

Abstract: We show that the asymptotic number of graphical sequences can be expressed in terms of Walkup’s formula for the number of plane trees. This yields a more detailed description of the asymptotics by Balister, Donderwinkel, Groenland, Johnston and Scott. Our proof is probabilistic, using what we call the Lévy–Khintchine method. We will discuss other applications of this method, and connections with additive number theory (subset counting formulas by von Sterneck and the Erdös–Ginzburg–Ziv theorem). Joint work with Michal Bassan (Oxford) and Serte Donderwinkel (Groningen).

Analysis on 14 November 2024 at 16:00

Speaker: Annalisa Massaccesi (University of Padova)
Title: Constructions for a C^1 function with prescribed gradient on a Cantor-type set

Abstract: In this talk I will outline the iterative construction of a C^1 function u, with \|u\|_\infty \leq \eta and Du(x)=F(x,u(x)) on a Cantor-type set C. It is transparent from the construction the presence of a trade off between the size of C and the Hölder regularity of Du. This type of construction is the building block for counterexamples to Frobenius theorem when the tangency set is not regular enough.

Statistical Mechanics on 14 November 2024 at 14:00

Speaker: Jakob Björnberg (University of Gothenburg/Chalmers)
Title: Dimerisation in mirror models and quantum spin chains

Abstract: We consider two models of random loops where we prove breaking of translational symmetry. The first is a mirror model, where the loops are formed by light rays bouncing in a labyrinth of randomly oriented mirrors. The second is a probabilistic representation of a quantum spin chain, and can be obtained as a limit of the first, for inhomogeneous mirror weights. In the terminology of quantum spins, this symmetry-breaking is called “dimerisation”. Based on joint works with K. Ryan as well as with P. Muehlbacher, B. Nachtergaele and D. Ueltschi.

Geometry and Topology on 14 November 2024 at 13:30

Speaker: Mikhail Hlushchanka (University of Amsterdam)
Title: Canonical decomposition of rational maps

Abstract: There are various classical and more recent decomposition results in mapping class group theory, geometric group theory, and complex dynamics (which include celebrated results by Bill Thurston). The goal of this talk is to introduce a powerful decomposition of rational maps based on the topological structure of their Julia sets. Namely, we will discuss the following result: every postcritically-finite rational map with non-empty Fatou set can be canonically decomposed into crochet maps (these have very "thinly connected" Julia sets”) and Sierpinski carpet maps (these have very "heavily connected" Julia sets). If time permits, I will discuss applications of this result in various aspects of geometric group theory. Based on a joint work with Dima Dudko and Dierk Schleicher.

Algebra on 14 November 2024 at 12:00

Speaker: Charley Cummings (Aarhus)
Title: Metric completions of cluster categories

Abstract: The completion of a metric space is a classical method for generating new mathematical structures from old. Recently, Neeman emulated this idea to define a metric completion of a triangulated category, thereby providing a novel way to construct new triangulated categories. However, computing these completions often requires using the properties of an already completed ambient category, like the derived category. In this talk, based on joint work with Sira Gratz, we present an example from cluster theory that avoids this requirement by focusing on categories that have combinatorial models, and show that their categorial completions can be viewed as topological completions of the associated models.

Algebraic Geometry on 13 November 2024 at 15:00

Speaker: Tiago Duarte Guerreiro (Paris-Saclay)
Title: On hypersurfaces in projective bundles

Abstract: Mori dream spaces are a special kind of varieties introduced by Hu and Keel in 2000 that enjoy very good properties with respect to the minimal model program. On the other hand, not many classes of examples of these are known. In this talk we introduce general hypersurfaces in certain projective bundles of Picard rank 2 and show that (some of) these are Mori dream spaces, partially generalising Ottem's result on hypersurfaces in products of projective spaces.

Algebraic Topology on 12 November 2024 at 17:00

Speaker: John Greenlees (University of Warwick)
Title: An algebraic model for rational SU(3)-spectra in 18 blocks

Abstract: For each compact Lie group G, one may hope to construct an algebraic category A(G) which is Quillen equivalent to the category of rational G-equivariant cohomology theories. A(G) takes the form of a category of sheaves over a space X_G of conjugacy classes of subgroups of G. When G is SU(3) there is a partition of X_G into 18 blocks, over each of which one may make A(G) explicit. This example is small enough to be explicit and large enough to illustrate some general techniques.

Number Theory on 11 November 2024 at 15:00

Speaker: Chris Daw (University of Reading)
Title: Large Galois orbits under multiplicative degeneration

Abstract: The Pila-Zannier strategy is a powerful technique for proving results in unlikely intersections. In this talk, I will recall the Zilber-Pink conjecture for Shimura varieties and describe how Pila-Zannier works in this setting. I will highlight the most difficult outstanding obstacle to implementing the strategy — the so-called Large Galois Orbits conjecture — and I will explain recent progress towards this conjecture, building on the works of André and Bombieri. This is joint with Martin Orr (Manchester).

SBIDER on 11 November 2024 at 14:00

Speaker: Laura Wadkin (Newcastle University)
Title: Modelling the spread of tree diseases and invasive pests through UK treescapes

Abstract: The loss of biodiversity due to the spread of destructive tree diseases and invasive pests within our native forests is having an enormous environmental, economic, and social impact. In the ‘25 Year Environment Plan’ the UK government highlights enhancing biosecurity as a key priority, through the control of existing diseases and pests, and by building forest resilience against new ones. We are working in collaboration with Defra to develop mathematical models to deepen our understanding of the fundamental behaviours of key pests and pathogens, act as predictive tools for forecasting, and to explore different control strategies. Broadly, we use a combination of partial differential equations, agent-based modelling, and statistical inference techniques. In this talk I will give an overview of the collaborative work to date and present a case study example of the oak processionary moth epidemic in London parks to show how the parameters for a compartmental SIR model with a time varying infection rate can be inferred.

Colloquium on 08 November 2024 at 16:00

Speaker: Stefan Güttel (Manchester)
Title: Randomized algorithms in numerical linear algebra

Abstract: Randomization is an established technique to speed up the numerical solution of very large-scale linear algebra problems that have some form of redundancy, with overdetermined least-squares problems and low-rank matrix approximation being the most prominent examples. Until recently, it has been less clear how to apply randomization to problems that do not have inherent redundancy, including linear systems of equations, matrix functions, and (non)linear eigenvalue problems. I will discuss some new ideas to speed up computational methods for these problems.

Combinatorics on 08 November 2024 at 14:00

Speaker: Matías Pavez-Signé (University of Chile)
Title: Ramsey numbers of cycles in random graphs

Abstract: Let C_n denote the cycle on n vertices. We say a graph G is C_n-Ramsey if every 2-colouring of the edges of G contains a monochromatic copy of C_n. The classical Ramsey problem for cycles asks for determining the minimum number R(C_n) so that the complete graph on R(C_n) vertices is C_n-Ramsey. This talk will study when a random graph G(N,p) is C_n-Ramsey with high probability. In particular, we will show that even for very sparse edge probability p and N quite close to R(C_n), G(N,p) remains C_n-Ramsey.

Analysis on 07 November 2024 at 16:00

Speaker: Marco Pozzetta (Polytechnic University of Milan)
Title: On the uniqueness of isoperimetric sets on manifolds with nonnegative curvature

Abstract: We consider the isoperimetric problem, that is the minimization of the measure of the boundary among subsets having a given volume, on noncompact manifolds with nonnegative Ricci curvature, Euclidean volume growth and with quadratic Riemann curvature decay. The aim of the talk is to discuss uniqueness and stability properties of minimizers, called isoperimetric sets. Assuming the manifold is not the Euclidean space, we show that for most large volumes (in a quantified way) there exists a unique isoperimetric set, and its boundary is strictly volume preserving stable. Uniqueness here is meant in the set theoretical sense and it is not understood up to isometry of the ambient. We show with a counterexample that the result cannot be improved to uniqueness or strict stability for every large volume. The lack of higher regularity at infinity prevents the application of classical methods based on the implicit function theorem. A key tool for deriving the needed effective estimates on the Jacobi operator of the boundary of large isoperimetric sets is provided here by the sharp concavity property of the isoperimetric profile function, which will be briefly reviewed. The talk is based on a joint work with Gioacchino Antonelli and Daniele Semola.

Statistical Mechanics on 07 November 2024 at 14:00

Speaker: Barbara Roos (University of Tübingen)
Title: Macroscopic Thermalization for Highly Degenerate Hamiltonians

Abstract: A closed quantum system thermalizes in the sense of typicality, if any initial state will reach a suitable equilibrium subspace and stay there most of the time. For non-degenerate Hamiltonians, a sufficient condition for thermalization is the eigenstate thermalization hypothesis (ETH). Shiraishi and Tasaki recently proved the ETH for a perturbation of the Hamiltonian of free fermions on a one-dimensional lattice. The perturbation is needed to remove the high degeneracies of the Hamiltonian. We point out that also for degenerate Hamiltonians ETH implies thermalization. Additionally, we develop another strategy for proving thermalization by adding small generic perturbations. This is joint work with Stefan Teufel, Roderich Tumulka, and Cornelia Vogel.

Geometry and Topology on 07 November 2024 at 13:30

Speaker: Sami Douba (IHES)
Title: Zariski closures of linear reflection groups

Abstract: We show that linear reflection groups in the sense of Vinberg are often Zariski dense in PGL(n). Among the applications are examples of low-dimensional closed hyperbolic manifolds whose fundamental groups virtually embed as Zariski-dense subgroups of SL(n,Z), as well as some one-ended Zariski-dense subgroups of SL(n,Z) that are finitely generated but infinitely presented, for all sufficiently large n. This is joint work with Jacques Audibert, Gye-Seon Lee, and Ludovic Marquis.

Algebra on 07 November 2024 at 12:00

Speaker: Chris Bowman (University of York)
Title: A combinatorial introduction to Hecke Categories

Abstract: Hecke categories control the representation theory of symmetric and algebraic groups, and generalise this theory from Weyl groups to all parabolic Coxeter systems. We give an introductory survey of some of the recent results in this area from a concrete combinatorial point of view.

Algebraic Geometry on 06 November 2024 at 15:00

Speaker: Tarig Abdelgadir (Loughborough University)
Title: The McKay correspondence via VGIT (case D4)

Abstract: For a Kleinian singularity, the McKay correspondence famously relates the orbifold cover of the singularity to a crepant resolution. In type A, both are toric and it is easy to write down a GIT problem which produces both the orbifold and the geometric resolution as possible quotients. However, no such construction seems to be known for types D and E. I'll describe how we fill this gap for the simplest non-trivial case D4. The construction is inspired by Tannaka duality and sets out a strategy to tackle general types D and E. This is joint work with Ed Segal.

Mathematics Teaching and Learning on 06 November 2024 at 14:00

Speaker: Beatriz Navarro Lameda (UCL)
Title: Online Assessment Platforms: Crowdmark Demo

Abstract: Crowdmark is an online assessment platform that helps educators assess student work more effectively. This tool allows you to mark two to three times faster compared to marking paper exams while at the same time leaving richer feedback for students. It supports LaTeX and Markdown formatting, multiple choice questions (marked automatically) and longer questions for which student can submit scanned handwritten answers. Crowdmark supporting both online assessments and in-person, paper-based exams that can be scanned for digital marking. The ability to mark paper-based exams online is especially beneficial for department that frequently administer in-person exams, such as maths and stats departments. In this demo, I’ll walk you through the essentials of using Crowdmark. I’ll cover how to set up assessments and create questions, guide students through the submission process, and leverage Crowdmark’s features to maximise marking efficiency. Additionally, I’ll demonstrate how to create a workflow for delivering and marking in-person exams with Crowdmark.

Algebraic Topology on 05 November 2024 at 17:00

Speaker: Marco La Vecchia (Warwick)
Title: Twisted equivariant Chern Classes and Equivariant Formal Group Laws

Abstract: Chern classes are classical invariants that play a fundamental role in the study of vector bundles. Recently, Schwede introduced U(n)-equivariant Chern classes within the context of equivariant bordism. In this talk, I will extend this framework by defining G-twisted equivariant Chern classes in the setting of G \times U(n)-equivariant bordism. I will then explore the connection between these twisted equivariant Chern classes and the theory of G-equivariant formal group laws, where G is any compact Lie group.

Partial Differential Equations and their Applications on 05 November 2024 at 12:00

Speaker: Lorenzo Pareschi (Heriot Watt)
Title: TBA

Abstract: TBA

Number Theory on 04 November 2024 at 15:00

Speaker: Andrei Yafaev (University College London)
Title: TBA

Abstract: TBA

DAGGER on 04 November 2024 at 14:00

Speaker: Eduardo Silva (University of Münster)
Title: Harmonic functions on groups and the Poisson boundary

Abstract: The Poisson boundary of a countable group [latex alt='g']$G$[/latex] endowed with a probability measure [latex alt='g']$\mu$[/latex] is a probability space that encodes all bounded [latex alt='g']$\mu$[/latex]-harmonic functions on the group. Alternatively, it captures the asymptotic directions of the [latex alt='g']$\mu$[/latex]-random walk on the group. A natural problem is to identify an explicit model of the associated Poisson boundary, described in terms of the geometry of [latex alt='g']$G$[/latex]. In this talk I will give an introduction to the theory of Poisson boundaries, discuss the identification problem for diverse classes of groups, and explain the connections with entropy. I will concentrate on joint work with Joshua Frisch, where we identify the Poisson boundary of lamplighter groups [latex alt='g']$A \wr \mathbb{Z}^d$[/latex], for [latex alt='g']$d\geq 3$[/latex] and [latex alt='g']$A$[/latex] any countable group, for probability measures with finite entropy and that satisfy a stabilization condition that naturally arises in this context.

SBIDER on 04 November 2024 at 14:00

Speaker: Xander O'Neill (Heriot-Watt University)
Title: Pathogen persistence in wildlife populations

Abstract: How do highly virulent pathogens persist? We start by delving into the dynamics of African swine fever, a highly virulent pathogen, which can be sustained in a wild boar population despite a mortality rate of 90-100%. How does this persist? How could the introduction of this virus impact other, more chronic illnesses, such us tuberculosis? Can the lack of control for one make it easier to control or eradicate the other? This comes full circle when we propose a more general study, asking the question, what key model characteristics lead to slower (or faster) approximate times to extinction?

Soft Matter Lunches on 04 November 2024 at 12:00

Speaker: Michiko Shimokawa (Nara Women's University, Nara, Japan)
Title: Bifurcation of rotational motion of an elliptical camphor-coated disk

Abstract: A camphor boat is one of the famous self-propelled particles, which moves spontaneously on the water due to the difference in surface tension around the boat. The collective motions of the camphor boats resemble traffic jams and the quorum sensing in living things, and the camphor boat has been studied as an example of an active matter in non-biological systems. Furthermore, the camphor boat has been interesting topics as bifurcation phenomena, where the behaviour changes drastically at a certain value of the parameter. When an elliptical camphor disk, with the center of mass fixed at the axis of rotation, is placed on the surface of water, it rotates spontaneously. We found the appearance of the bifurcation from the stable state to the rotational state in the control of the water depth. The bifurcation type, which is subcritical bifurcation or supercritical bifurcation, depended on the aspect ratio of the elliptical camphor disk. We discussed the important factor to determine the bifurcation type through the results of our experimental results and our phenomenological model.

Colloquium on 01 November 2024 at 16:00

Speaker: Harry Schmidt (Warwick)
Title: Canonical heights and equidistribution

Abstract: Algebraic numbers are roots of (non-zero) polynomials with coefficients in the integers. We can measure their size with a height function. There are various height functions associated to geometric and dynamical objects, and I will give some examples coming from dynamical systems induced by polynomial maps. I will present some joint work with Philipp Habegger in which we prove lower bounds for such heights and give some applications of our work. Time permitting, I will also present some joint work with Myrto Mavraki in which we study points that are small with respect to two distinct heights.

Combinatorics on 01 November 2024 at 14:00

Speaker: Marius Tiba (King's College London)
Title: Upper bounds for multicolour Ramsey numbers

Abstract: The $r$-colour Ramsey number $R_r(k)$ is the minimum $n \in \mathbb{N}$ such that every $r$-colouring of the edges of the complete graph $K_n$ on $n$ vertices contains a monochromatic copy of $K_k$. We prove, for each fixed $r \geqslant 2$, that $$R_r(k) \leqslant e^{-\delta k} r^{rk}$$ for some constant $\delta = \delta(r) > 0$ and all sufficiently large $k \in \mathbb{N}$. For each $r \geqslant 3$, this is the first exponential improvement over the upper bound of Erd\H{o}s and Szekeres from 1935. In the case $r = 2$, it gives a different proof of a recent result of Campos, Griffiths, Morris and Sahasrabudhe. This is based on joint work with Paul Balister, B\'ela Bollob\'as, Marcelo Campos, Simon Griffiths, Eoin Hurley, Robert Morris and Julian Sahasrabudhe.

Analysis on 31 October 2024 at 16:00

Speaker: Max Goering (Jyvaskyla)
Title: Tangents and rectifiability in a rough Riemannian setting

Abstract: This talk will introduce $\Lambda$-tangents, a recent extension of Preiss' tangent measures which adapt tangent measure techniques to the study of elliptic problems. We then discuss forthcoming results using $\Lambda$-tangents to characterize rectifiable measures in terms of singular integrals. The relationship between (these) singular integrals, PDEs, and the geometry of measures is then developed. Finally, we remark on some new insights and open questions resulting from this joint work with Emily Casey, Tatiana Toro, and Bobby Wilson.

Mathematics Teaching and Learning on 31 October 2024 at 16:00

Speaker: Mojca Premuš (University of Ljubljana)
Title: Bridging the Gap: A Strategic Refresher Course in Mathematics

Abstract: This presentation outlines the structure and objectives of a non-compulsory, intensive one-week refresher course designed to bridge the gap between high school and university-level mathematics for incoming engineering students at the University of Ljubljana. The course includes an entry test. It also offers two levels of difficulty. The aim is to reinforce foundational mathematical concepts and enhance students’ readiness for the rigorous demands of their academic programs. Additionally, the presentation will highlight the innovative use of e-classrooms and STACK questions to facilitate interactive learning and continuous assessment. Note: Prof. Premuš will also be giving a short presentation on the University of Ljubljana.

Geometry and Topology on 31 October 2024 at 13:30

Speaker: Stefanie Zbinden (Heriot-Watt University)
Title: Morse directions in classical small cancellation groups

Abstract: Morse geodesics are geodesics that capture the hyperbolic-like features of not necessarily hyperbolic spaces. They were studied in order to generalize proofs about hyperbolic groups. However, it quickly became clear that having a Morse geodesic is not enough to exclude various types of pathological behaviours, which makes many genearlizations impossible. Luckily, it turns out that having slightly stronger assumptions on the group, such as having a WPD element or being "Morse-local-to-global" makes certain pathologies impossible. In this talk, we explore how those stronger assumptions relate to each other in the case of small cancellation groups.

Algebra on 31 October 2024 at 12:00

Speaker: Evgeny Khukhro (University of Lincoln)
Title: Engel sinks in finite, profinite, and compact groups

Abstract: Using Zelmanov's deep results on Engel Lie algebras, Wilson and Zelmanov proved that any profinite Engel group is locally nilpotent, and Medvedev extended this result to Engel compact groups. We state generalizations of the Engel condition as restrictions on the so-called Engel sinks of group elements. For example, a group can be considered to be `almost Engel' if all Engel sinks are finite. We proved that almost Engel compact groups are almost locally nilpotent (in certain precise terms). Similar results for finite groups have quantitative nature, with almost nilpotency expressed as a function of sizes of Engel sinks. Our most recent results concern imposing restrictions on Engel sinks of commutators (rather than all elements). This is joint work with Pavel Shumyatsky.

Algebraic Topology on 29 October 2024 at 17:00

Speaker: Matt Booth (Imperial College London)
Title: Calabi-Yau structures and Koszul duality

Abstract: I'll give a reminder of Koszul duality, before talking about a generalised notion of Calabi-Yau structure for dg (co)algebras and indicating why it is Koszul dual to a symmetric Frobenius condition. There is also an analogous one-sided version: Gorenstein (co)algebras are Koszul dual to Frobenius (co)algebras. This leads to a surprising example: the ring k[[x]] of formal power series, equipped with its natural topology, is a pseudocompact Frobenius algebra. As an application of the above theory, we obtain a new characterisation of Poincaré duality spaces, which for simply connected spaces recovers Félix-Halperin-Thomas's notion of Gorenstein space. This is joint work with Joe Chuang and Andrey Lazarev, to appear on the ArXiv soon.

Ergodic Theory and Dynamical Systems on 29 October 2024 at 14:15

Speaker: Alexey Korepanov (Loughborough)
Title: Memory loss near the boundary of null recurrence for Harris recurrent Markov chains and infinite measure preserving intermittent dynamical systems

Abstract: I'll talk about our joint work in progress with Ilya Chevyrev. Memory loss is a quantification of how quickly an evolving system forgets its initial state. For example, for a Markov chain with transition operator P, given two probability measures mu and nu, we may want to know how quickly the distance between P^n mu and P^n nu decays in total variation. For Markov chains with slow (polynomial) recurrence, memory loss has been very well understood half a century ago (starting with Orey or Pitman) as long the chain is positive recurrent, yet we could not find any results in the null recurrent case (even though related questions are a subject of well developed Renewal Theory). A similar situation takes place in chaotic dynamical systems. I'll present (first?) results on memory loss that work for positive as well as null recurrent systems, taking a particular interest in proofs that survive the transition between positive and null recurrence.

Partial Differential Equations and their Applications on 29 October 2024 at 12:00

Speaker: Esther Bou-Dagher (Paris Dauphine)
Title: TBA

Abstract: TBA

Number Theory on 28 October 2024 at 15:00

Speaker: Akshat Mudgal (Warwick)
Title: Recent progress towards the sum–product conjecture and related problems

Abstract: An important open problem in combinatorial number theory is the Erdős–Szemerédi sum–product conjecture, which suggests that for any positive integers s, N, and for any set A of N integers, either there are many s-fold sums of the form $a_1 + … + a_s$ or there are many s-fold products of the form $a_1\dots a_s$. While this remains wide open, various generalisations of this problem have been considered more recently, including the question of finding optimal variations of the so-called low energy decompositions. In this talk, I will outline some recent progress towards the above questions, as well as highlight how these connect very naturally to other key conjectures in additive combinatorics.

SBIDER on 28 October 2024 at 14:00

Speaker: Anne Skeldon (University of Surrey)
Title: Mathematical modelling of the sleep-wake cycle: light, clocks and digital-twins

Abstract: We all sleep. But what determines when and for how long? In this talk I’ll describe some of the fundamental mechanisms that regulate sleep. I’ll introduce the nonsmooth coupled oscillator systems that form the basis of current mathematical models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we are using models to unravel environmental, societal and physiological factors that determine sleep timing and outline how constructing digital-twins could enable us to create personalised light interventions for sleep timing disorders.

Combinatorics on 25 October 2024 at 14:00

Speaker: Sarah Selkirk (University of Warwick)
Title: Directed lattice paths with negative boundary

Abstract: Given a set $\mathcal{S} \subseteq \{1\}\times \mathbb{Z}$, a directed lattice path with stepset $\mathcal{S}$ is a finite sequence whose elements are in $\mathcal{S}$. Visually, the elements of the sequence are drawn as vectors starting at $(0, 0)$. Further restrictions, or a lack thereof, on the height of $y$-coordinates ($y\geq 0$) and end-point ($y=0$) of the sequence result in a classification of paths into the four main varieties of lattice path: walks, bridges, meanders, and excursions. For these families, generating functions have been derived in general in the influential work of Banderier and Flajolet (2002) by means of the kernel method. In recent years, directed lattice paths with height restriction $y \geq -t$ with $t\in \mathbb{N}$ have been connected to a number of other combinatorial objects, but have not yet been studied in general. In this talk, we discuss first enumerative results towards a general Banderier-Flajolet-style result for paths with a negative boundary.

Statistical Mechanics on 24 October 2024 at 14:00

Speaker: Juan Neirotti (Aston University)
Title: Legislative impeachments in a neural network society

Abstract: Inspired by studies of government overthrows in modern South American presidential democracies, we present an agent-based Statistical Mechanics analysis of the coordinated actions of strategic political actors within legislative chambers and the conditions that can lead to premature changes in executive leadership, such as presidential impeachments or motions of no confidence in prime ministers. The legislative actors are modeled as information-processing agents, equipped with neural networks, who express opinions on issues from the presidential agenda. We construct a Hamiltonian representing the collective cost incurred by agents for holding a particular set of opinions from a range of possible stances. Using replica methods, we explore two types of disorder: in the distribution of neural network weights and in the structure of agent interactions. The resulting phase diagram illustrates how control parameters -- loosely interpreted as indices of legislative strategic support, presidential polling popularity, and the volume of issues on the presidential agenda -- govern the system behavior. The model reveals an intermediate phase where strategic behaviors in support of or against the executive coexist, flanked by phases (characterised by a pure state) where the legislative vote aligns fully with either supporting or opposing the executive. Changes in these indices, driven by external factors, can push the system out of the coexistence phase and into the opposing pure phase, triggering a phase transition that leads to the removal of the executive through constitutional means. Using data from Brazil, we analyze presidential trajectories during the democratic period starting in 1989, showing that these trajectories align with the phase diagram in terms of whether the president was removed or remained in office.

Algebra on 24 October 2024 at 12:00

Speaker: Alice Dell'Arciprete (University of York)
Title: Quiver presentations for Hecke categories and KLR algebras

Abstract: We discuss the algebraic structure of KLR algebras by way of the diagrammatic Hecke categories of maximal parabolics of finite symmetric groups. Combinatorics (in the shape of Dyck tableaux) plays a huge role in understanding the structure of these algebras. Instead of looking only at the sets of Dyck tableaux (which enumerate the q-decomposition numbers) we look at the relationships for passing between these Dyck tableaux. In fact, this “meta-Kazhdan-Lusztig combinatorics” is sufficiently rich as to completely determine the complete Ext-quiver and relations of these algebras.

One day ergodic theory meeting on 23 October 2024 at 16:45

Speaker: Meng Wu (Oulu)
Title: On normal numbers in fractals

Abstract: Given any Bernoulli measure μ that is x3 invariant (such as the Cantor-Lebesgue measure on the ternary Cantor set) and an irrational number t, it holds that for almost all x with respect to μ, the product tx is x3 normal (meaning that the orbit of tx under the x3 map is uniformly distributed on [0,1]). This result was recently proved by Dayan, Ganguly, and Barak Weiss using techniques from random walk theory. We will present a new proof of the Dayan-Ganguly-Weiss result, relying on recent advancements in the study of self-similar measures with overlaps. Our approach extends the result to cases where the measure μ is only required to be invariant, ergodic, and of positive dimension.

One Day Ergodic Theory Meeting on 23 October 2024 at 15:30

Speaker: Tanja Schindler (University of Exeter)
Title: A qualitative central limit theorem for certain unbounded observables over piecewise expanding interval maps

Abstract: Many limit theorems in ergodic theory are proven using the spectral gap method. So one of the main ingredients for this method is to have a space on which the transfer operator has a spectral gap. However, most of the classical spaces, like for example the space of Hölder or quasi-Hölder function or BV functions, don't allow unbounded functions. We will give such a space which allows observables with a pole at the fixed points of a piecewise expanding interval transformation and state a quantitative central limit theorem using Edgeworth expansions. As an application we give a sampling result for the Riemann-zeta function over a Boolean type transformation. This is joint work with Kasun Fernando.

Algebraic Geometry on 23 October 2024 at 15:00

Speaker: Will Donovan (Tsinghua University)
Title: Derived symmetries for crepant resolutions of hypersurfaces

Abstract: Given a singularity with a crepant resolution, a symmetry of the derived category of coherent sheaves on the resolution may often be constructed using the formalism of spherical functors. I will introduce this, and new work (arXiv:2409.19555) on general constructions of such symmetries for hypersurface singularities. This builds on previous results with Segal, and is inspired by work of Bodzenta-Bondal.

One Day Ergodic Theory Meeting on 23 October 2024 at 14:00

Speaker: Mike Hochman (HUJI)
Title: Strongly irreducible subshifts without periodic points

Abstract: A symbolic system is strongly irreducible if there is some g>0 such that any two patterns in the subshift can be glued together as long as they are separated by a gap of size g. This is the strongest mixing condition one can place on a symbolic system, and it implies many good properties, especially in combination with the finite type property: For example, globally supported measures of maximal entropy, a Krieger-type embedding theorem, and more. In my talk I will discuss the question of the existence of periodic points in such systems, and its connection to a question about periodic points in higher-dimensional shifts of finite type.

Soft Matter Lunches on 23 October 2024 at 13:00

Speaker: Matthew Butler (UCL)
Title: Modelling mechanics of material replacement in biological systems

Abstract: Many biological systems contain material components that are repaired and replaced over time by accompanying cells. One common example is the extra-cellular matrix, an interconnected network of proteins that provides chemical and mechanical protection and support in many systems, such as tissue basement membranes and bacterial biofilms. Questions remain as to how the bulk mechanical properties of the material depend on cell maintenance. I will present a spring-based model that aims to capture how the microscale replacement of elastic material can give rise to different observed bulk mechanical behaviours. Despite the model’s simplicity, it has a number of interesting characteristics that are biologically-relevant.

Algebraic Topology on 22 October 2024 at 17:00

Speaker: Ming Ng (Queen Mary University of London)
Title: K1(Var) is generated by Quasi-Automorphisms

Abstract: Our understanding of K-theory is changing. In recent years, much work has been done to extend various tools from algebraic K-theory to various non-additive settings. One particular highlight: in the same way one can define the K-theory spectrum of an exact category, one can construct a K-theory spectrum K(Var) recovering the Grothendieck ring of varieties as ¥pi_0 [Zakharevich, Campbell]. Up until recently, no complete characterisation of K_n(Var) was known except for n=0. This talk will discuss a new result that shows K_1(Var) is generated by an interesting generalisation of automorphisms of varieties, and present its full relations. In our language: given any pCGW category C (a generalisation of exact categories that also includes finite sets, varieties, definable sets, etc.), the group K1(C) is generated by double exact squares (which we also call quasi-automorphisms). Time permitting, we discuss future applications, as well as a technical subtlety regarding how composition of 1-simplices split in K1(Var), and compare this with Zakharevich’s original presentation of K1(Var).

Ergodic Theory and Dynamical Systems on 22 October 2024 at 13:00

Speaker: Thomas Jordan (University of Bristol)
Title: Countable Markov shifts, pressure at infinity and large deviations

Abstract: For an ergodic transformation, large deviations measure the rate of the decay of the measure of the points where the Birkhoff average is away from the expected value. For many hyperbolic dynamical systems with Gibbs measures this rate is exponential and the exponential rate can be determined using a suitable pressure function. We will show how these results can be adjusted to the setting of mixing subshifts where the alphabet is countably infinite. We show how the standard results can be adapted to this setting and related to the concept of pressure at infinity (recently introduced by Anibal Velozo). We show how the pressure at infinity interplays with the standard rate function and also show a version of large deviations where the rate functions come directly from the pressure at infinity. This is joint work with Godofredo Iommi and Anibal Velozo.

Partial Differential Equations and their Applications on 22 October 2024 at 12:00

Speaker: Richard Medina (Paris Dauphine)
Title: TBA

Abstract: TBA

Number Theory on 21 October 2024 at 15:00

Speaker: Tobias Berger (University of Sheffield)
Title: Pseudomodularity of residually reducible Galois representations

Abstract: After a survey of previous work I will present new results on pseudomodularity of residually reducible Galois representations with 3 residual pieces. I will discuss applications to proving modularity of Galois representations arising from abelian surfaces and Picard curves. This is joint work with Krzysztof Klosin (CUNY).

SBIDER on 21 October 2024 at 14:00

Speaker: Denis Patterson (University of Durham)
Title: Spatial models of forest-savanna bistability

Abstract: Empirical studies suggest that for vast tracts of land in the tropics, closed-canopy forests and savannas are alternative stable states, a proposition with far-reaching implications in the context of ongoing climate change. Consequently, numerous spatially implicit and explicit mathematical models have been proposed to capture the mechanistic basis of this bistability and quantify the stability of these ecosystems. We present an analysis of a spatially extended version of the so-called Staver-Levin model of forest-savanna dynamics (a system of nonlinear partial integro-differential equations). On a homogeneous domain, we uncover various types of pattern-forming bifurcations in the presence of resource limitation, which we study as a function of the resource constraints and length scales in the problem. On larger (continental) spatial scales, heterogeneity plays a significant role in determining observed vegetative cover. Incorporating domain heterogeneity leads to interesting phenomena such as front-pinning, complex waves, and extensive multi-stability, which we investigate analytically and numerically.

Colloquium on 18 October 2024 at 16:00

Speaker: Liz Fearon (UCL)
Title: Epidemiological modelling of testing, contact tracing and isolation interventions in epidemic response: experiences from COVID-19

Abstract: This talk will explore mathematical modelling used to support design and deployment decisions for one of our key epidemic control interventions: testing, tracing and isolation or quarantine (TTI). I will review the types of questions that were posed at different stages of the COVID-19 pandemic in the UK and how we responded to them, highlighting the types of modelling tools that were used. Thinking more broadly and looking forward, I will consider new challenges, including for other types of infections and learnings for how we develop models and engage with communities and other disciplines in doing so.

Combinatorics on 18 October 2024 at 14:00

Speaker: Camila Zárate-Guerén (University of Birmingham)
Title: Colour-bias perfect matchings in hypergraphs

Abstract: Given a k-uniform hypergraph H on n vertices with an r-colouring of its edges, we look for a minimum l-degree condition that guarantees the existence of a perfect matching in H that has more than n/rk edges in one colour. We call this a colour-bias perfect matching. For 2-coloured graphs, a result of Balogh, Csaba, Jing and Pluhár yields the minimum degree threshold that ensures a perfect matching of significant colour-bias. In this talk, I will present an analogous of this result for k-uniform hypergraphs. More precisely, for each 1<=l<k and r>=2 we determined the minimum l-degree threshold that forces a perfect matching of significant colour-bias in an r-edge-coloured k-uniform hypergraph. The presented result is joint work with J. Balogh, H. Hàn, R. Lang, J. P. Marciano, M. Pavez-Signé, N. Sanhueza-Matamala and A. Treglown.

Analysis on 17 October 2024 at 16:00

Speaker: Emily Casey (University of Washington)
Title: Characterizing rectifiability in terms of principal values

Abstract: Since the work of Mattila and Preiss in 1995, it's been known that for a Radon measure with reasonable density assumptions, the almost everywhere existence of principal values of the Riesz transform is equivalent to the measure being rectifiable. In ongoing work with Goering, Toro, and Wilson, we extend this result of Mattila and Preiss to a rough Riemannian setting. In this talk, we discuss the techniques used in proving the almost everywhere existence of principal values for smooth Calderon Zygmund kernels for rectifiable measures, even when the kernel is not of convolution type.

Geometry and Topology on 17 October 2024 at 13:30

Speaker: Mireille Soergel (MPIM Leipzig)
Title: Dyer groups: Coxeter groups, right-angled Artin groups and more...

Abstract: Dyer groups are a family encompassing both Coxeter groups and right-angled Artin groups. Among many common properties, these two families admit the same solution to the word problem. Each of these two classes of groups also have natural piecewise Euclidean CAT(0) spaces associated to them. In this talk I will introduce Dyer groups, give some of their properties.

Algebra on 17 October 2024 at 12:00

Speaker: Jack Saunders (University of Bristol)
Title: Linear groups acting 4-arc-transitively on cubic graphs

Abstract: In this talk, we give a brief overview of s-arc-transitive graphs and show how their study in the case of cubic (3-regular) graphs reduces to a generation problem for finite almost simple groups. We then discuss current progress towards solving this generation problem for PSL(n,q) when n is sufficiently large and q is coprime to 6.

Ada Lovelace Day on 16 October 2024 at 14:00

Speaker: Various speakers (N/A)
Title: Ada Lovelace Day

Abstract: Ada Lovelace Day is an annual celebration of women's achievements in the fields of STEM. See https://warwick.ac.uk/fac/sci/maths/general/edi/ada_lovelace24/ for the schedule and more information. The event is open to all, irrespective of gender, so please do come along!

Algebraic Topology on 15 October 2024 at 17:00

Speaker: Robin Stoll (University of Cambridge)
Title: The stable cohomology of block diffeomorphisms of connected sums of S^k × S^l

Abstract: I will explain an identification of the stable rational cohomology of the classifying spaces of self-equivalences as well as block diffeomorphisms of connected sums of S^k × S^l (relative to an embedded disk), where 2 < k < l < 2k–1. The result is expressed in terms of versions of Lie graph complex homology, the constructions of which I will recall. This also leads to a computation, in a range of degrees, of the stable rational cohomology of the classifying spaces of diffeomorphisms of these manifolds. In the case l = k+1, this recovers and extends results of Ebert-Reinhold. If time permits, I will explain parts of the proof; this includes in particular work joint with Berglund on a certain type of algebraic models for relative self-equivalences of bundles, inspired by results of Berglund-Zeman.

Partial Differential Equations and their Applications on 15 October 2024 at 12:00

Speaker: Jakub Woznicki (Warsaw)
Title: TBA

Abstract: TBA

Number Theory on 14 October 2024 at 15:00

Speaker: Maleeha Khawaja (Sheffield)
Title: Galois groups of low degree points on curves

Abstract: Whilst the study of low degree algebraic points on curves is an active area of research, there has been little emphasis on the Galois-theoretic description of these points. In this talk, we focus on the behaviour of low degree points whose Galois group is primitive. Furthermore, we shall see that the behaviour changes if the degree is large (with respect to the genus of the curve). This talk is based on joint work with Frazer Jarvis (Sheffield) and Samir Siksek (Warwick).

DAGGER on 14 October 2024 at 14:00

Speaker: Mariam Al-Hawaj (Trinity College Dublin)
Title: Generalized pseudo-Anosov Maps and Hubbard Trees

Abstract: The Nielsen-Thurston classification of the mapping classes proved that every orientation preserving homeomorphism of a closed surface, up to isotopy is either periodic, reducible, or pseudo-Anosov. Pseudo-Anosov maps have particularly nice structure because they expand along one foliation by a factor of λ > 1 and contract along a transversal foliation by a factor of 1/λ. The number λ is called the dilatation of the pseudo-Anosov. Thurston showed that every dilatation λ of a pseudo-Anosov map is an algebraic unit, and conjectured that every algebraic unit λ whose Galois conjugates lie in the annulus A_λ = {z : 1/λ < |z| < λ} is a dilatation of some pseudo-Anosov on some surface S. Pseudo-Anosovs have a huge role in Teichmuller theory and geometric topology. The relation between these and complex dynamics has been well studied inspired by Thurston. In this project, I develop a new connection between the dynamics of quadratic polynomials on the complex plane and the dynamics of homeomorphisms of surfaces. In particular, given a quadratic polynomial, we show that one can construct an extension of it which is generalized pseudo-Anosov homeomorphism. Generalized pseudo-Anosov means the foliations have infinite singularities that accumulate on finitely many points. We determine for which quadratic polynomials such an extension exists. My construction is related to the dynamics on the Hubbard tree which is a forward invariant subset of the filled Julia set that contains the critical orbit.

SBIDER on 14 October 2024 at 14:00

Speaker: Emma Davis (University of Warwick)
Title: Applications of branching processes to disease emergence and elimination

Abstract: Branching processes can provide insights into the stochastic dynamics that can occur at low prevalence. We will discuss applications of these methods at opposite ends of the spectrum: 1) emerging outbreaks, with application to assessing the impact of contract tracing on control of COVID-19 in the UK; and 2) elimination, with application to assessing elimination thresholds for the Neglected Tropical Disease lymphatic filariasis.

Colloquium on 11 October 2024 at 16:00

Speaker: Mark Peletier (Eindhoven)
Title: In search of structure: Gradient flows, GENERIC systems, and the role of noise

Abstract: Many ODEs and PDEs describe real-world phenomena. Often it is useful to know that these equations have, more "structure" than that of the bare PDE. For instance, many ODEs and PDEs are Hamiltonian systems, which provides a wealth of additional information about their solutions. Other ODEs and PDEs are gradient flows, and this is the structure that I will concentrate on. Many evolutionary PDEs are known to be gradient flows in an appropriate sense, and again this property gives deep insight and provides many tools for analysis. Despite the importance of such gradient structures, it is only relatively recently that we have discovered the reason why many evolutionary PDEs are gradient flows, in particular why there are so many gradient flows based on the Wasserstein metric. It turns out that this is intimately connected to randomness. In this talk I will discuss gradient flows and their cousin "GENERIC systems", and show how one can understand how these deterministic, geometric structures have their roots in randomness.

Combinatorics on 11 October 2024 at 14:00

Speaker: Ella Williams (UCL)
Title: Covering vertices with monochromatic paths

Abstract: In 1995, Erd\H{o}s and Gy\'arf\'as proved that in every 2-edge-coloured complete graph on $n$ vertices, there exists a collection of $2\sqrt{n}$ monochromatic paths, all of the same colour, which cover the entire vertex set. They conjectured that it is possible to replace $2\sqrt{n}$ by $\sqrt{n}$. We prove this to be true for all sufficiently large $n$. This is based on joint work with Alexey Pokrovskiy and Leo Versteegen.

Geometry and Topology on 10 October 2024 at 13:30

Speaker: Shaked Bader (University of Oxford)
Title: Hyperbolic subgroups of type FP_2(Ring)

Abstract: In 1996 Gersten proved that if G is a word hyperbolic group of cohomological dimension 2 and H is a subgroup of type FP_2, then H is hyperbolic as well. In this talk, I will present a joint work with Robert Kropholler and Vlad Vankov generalising this result to show that the same is true if G is only assumed to have cohomological dimension 2 over some ring R and H is of type FP_2(R).

Soft Matter Lunches on 09 October 2024 at 13:00

Speaker: Nathan van der Riet (University of Warwick)
Title: Minimal modelling of vesiculation processes as drivers of topology change in cell membranes

Abstract: TBA

Number Theory on 07 October 2024 at 15:00

Speaker: Han Yu (University of Warwick)
Title: TBA

Abstract: TBA

DAGGER on 07 October 2024 at 14:00

Speaker: Short volunteered talks (University of Warwick)
Title: DAGGER welcome-back session

Abstract: DAGGER provides a space for early-career mathematicians with an interest in dynamics, geometry, topology, and related areas to share their research and connect over maths. Everyone — and in particular new PhD students, new master's students, and third-/fourth-year undergraduates — is invited to this introductory session of the DAGGER seminar, which will feature short (5-10 minute) volunteered talks. Come along to give a talk about something you find interesting, hear some maths, or just introduce yourself!

Partial Differential Equations and their Applications on 07 October 2024 at 14:00

Speaker: Clement Mouhot (Cambridge)
Title: TBA

Abstract: TBA

SBIDER on 07 October 2024 at 14:00

Speaker: Francesca Scarabel (University of Leeds)
Title: Numerical methods for structured population models in ecology and epidemiology

Abstract: In this talk I will consider mathematical models for populations where individual rates are completely determined by a continuous structuring variable that evolves in time (e.g. age or size in ecology, age or age of infection in epidemiology). They can be described as renewal equations or partial differential equations of transport type, and the set of software tools available for these types of equations is much more limited compared to that available for compartmental models formulated as ordinary differential equations (ODEs). In recent years, within a collaboration with the University of Udine (Italy), I have developed a series of user-friendly numerical methods to study the stability and bifurcations of structured population models by means of a convenient approximation with ODEs, which can be studied with well-established software for ODEs. More recently, similar numerical techniques have been used to obtain an efficient method to approximate the reproduction numbers. I will illustrate the methods with applications to mathematical ecology and epidemiology.

Combinatorics on 04 October 2024 at 14:00

Speaker: Akshat Mudgal (University of Warwick)
Title: Approximating sumset estimates via translates

Abstract: A finite, non-empty subset A of Z^d is defined to be d-dimensional if it is not contained in a translate of some hyperplane. Given a d-dimensional set A of cardinality N, a classical result in additive combinatorics known as Freiman’s lemma implies that |A+A| >= (d+1)N - d(d+1)/2. Moreover, this estimate is sharp. In the spirit of some recent work of Bollobas–Leader–Tiba, it is natural to ask whether one can approximate this lower bound by just considering a few translates of A. In joint work with Yifan Jing we prove precisely this, that is, for any d-dimensional set A with N elements, there exists a subset X of A with |X| = O_d(1) such that |A+X| >= (d+1)N - d(d+1)/2.

Geometry and Topology on 03 October 2024 at 13:30

Speaker: Saul Schleimer (University of Warwick)
Title: Solving the word problem in the mapping class group in quasi-linear time

Abstract: Mapping class groups of surfaces are of fundamental importance in dynamics, geometric group theory, and low-dimensional topology. The word problem for groups in general, the definition of the mapping class group, its finite generation by twists, and the solution to its word problem were all set out by Dehn [1911, 1922, 1938]. Some of this material was rediscovered by Lickorish [1960's] and then by Thurston [1970-80's] -- they gave important applications of the mapping class group to the topology and geometry of three-manifolds. In the past fifty years, various mathematicians (including Penner, Mosher, Hamidi-Tehrani, Dylan Thurston, Dynnikov) have given solutions to the word problem in the mapping class group, using a variety of techniques. All of these algorithms are quadratic-time. We give an algorithm requiring only O(n log^3(n)) time. We do this by combining Dynnikov's approach to curves on surfaces, M\"oller's version of the half-GCD algorithm, and a delicate error analysis in interval arithmetic. This is joint work with Mark Bell.

Mathematics Teaching and Learning on 02 October 2024 at 15:00

Speaker: Mani Mahal, Sam Petrie (Warwick)
Title: Exploring the use of AI in mathematics and statistics assessments: project outcome and highlights

Abstract: We will discuss highlights from the summer project studying the current use and future potential of generative AI in maths and stats at Warwick. Key questions include: 1. To what extent do our students currently use AI to help with assignments? 2. How well does AI perform in current assignments? 3. What future educational directions should our departments take given the rapid improvement of genAI?

Analysis on 01 October 2024 at 16:00

Speaker: Anna Skorobogatova (SLMath)
Title: Rectifiability of singularities and uniqueness of tangent cones for semicalibrated currents

Abstract: Semicalibrated currents are a subclass of almost area-minimizing surfaces appearing naturally in various geometric problems, and are a generalization of calibrated submanifolds. Unlike general almost area-minimizers, semicalibrated currents are expected to share the regularity properties of area-minimizing currents, and indeed it was shown by Spolaor in 2015 that the singular set is codimension two with respect to the surface, extending the conclusion of Almgren’s celebrated “big regularity paper” to this setting. I will talk about recent joint work with Paul Minter, Davide Parise and Luca Spolaor, in which we build on this to obtain a sharp structural result for the interior singular set, along with a classification of blow-ups at most singular points.

Junior Analysis and Probability Seminar on 30 September 2024 at 15:00

Speaker: Anna Skorobogatova (SLMath)
Title: Regularity for critical points of semilinear elliptic variational problems with a topological constraint

Abstract: I will discuss the regularity of critical points for a free boundary problem arising from the diffuse interface/Allen-Cahn approximation of the set-theoretic Plateau problem recently introduced by Maggi-Novack-Restrepo. Here, a homotopic spanning constraint, first considered by Harrison-Pugh, forces the surfaces (and also the corresponding interface for the diffuse approximation), to remain attached to the given wire frame. The presence of the spanning condition allows for minimizers of this problem to exhibit codimension 1 singularities such as triple junctions and tetrahedral singularities, in stark contrast to the work of Tonegawa-Wickramasekera which shows that any stable minimal hypersurface arising as a limit of interfaces for stable critical points of classical Allen-Cahn. I will further discuss free boundary regularity for minimizers of this problem. This is a joint work with Mike Novack (Louisiana State University) and Daniel Restrepo (Johns Hopkins University).

Number Theory on 30 September 2024 at 15:00

Speaker: Tim Browning (IST Austria)
Title: Pairs of commuting matrices

Abstract: I'll discuss commuting varieties and a new upper bound for the number of pairs of commuting $n \times n$ matrices with integer entries and height at most $T$, as $T \to \infty$. Our approach uses Fourier analysis and mod $p$ information, together with a result about the flatness of the commutator Lie bracket, which we also solve. This is joint work with Will Sawin and Victor Wang.

Soft Matter Lunches on 30 September 2024 at 12:00

Speaker: Joseph Webber (University of Warwick)
Title: Tubular hydrogel pumps through a responsive LENS

Abstract: Modelling thermo-responsive hydrogels can be a challenging task – the physics that underlies the rapid deswelling that occurs when temperatures cross a critical threshold is hard to characterise, and the transition from a swollen to a deswollen state involves the transport of fluid through the pores and the elastic deformation of the polymer scaffold left behind. In this talk, I will outline a new model for thermo-responsive gels that makes the physical processes behind deswelling straightforward to model and can reproduce all of the phenomenology seen in much more complicated energy-based approaches. This new model allows for the development of single-component displacement pumps that can drive flows of water through their lumen in response to pulses of heat, and we can deduce the optimum geometry for maximum pumping rates using the quantitative predictions that it provides.