Warwick Mathematics Institute Events
Seminar List Entry | Seminars by subject
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Junior Algebra Seminar on 19 October 2026 at 14:00 in B1.01, Zeeman Building
Speaker: Liam Hanany (University of Cambridge)
Title: Characteristic subgroup growth
Abstract: Given a finitely generated residually finite group Gamma, its subgroup growth type is the rate of growth of the function s_n(Gamma), counting the number of finite index subgroups in Gamma of index at most n. Various properties of the group Gamma can be read off of its subgroup growth type.
Let s_n^ch(Gamma) denote the number of finite index characteristic subgroups of Gamma, of index at most n. Answering a question of Igor Rivin, we compute the characteristic subgroup growth type of free groups, and more generally of large groups.
This talk is based on joint work with Alex Lubotzky. -
Number Theory on 19 October 2026 at 15:00 in B3.02
Speaker: Noah Kravitz (University of Oxford)
Title: The structure of sets with few subset sums
Abstract: An old result of Nathanson shows that every n-element set of positive reals has at least n(n+1)/2+1 distinct subset sums, with equality exactly for homogeneous arithmetic progressions. We establish stability versions of this inverse theorem in two regimes. First, for any parameter M at most n-4, we precisely characterize the n-element sets of positive reals with at most n(n+1)/2+1+M subset sums. Second, for any constant C, we provide a characterization, sharp up to constants, of the n-element sets of positive reals with at most Cn^2 subset sums. Joint work with Ruben Carpenter and Colin Defant.
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Algebraic Geometry on 21 October 2026 at 15:00 in B3.02
Speaker: Veronica Arena (University of Cambridge)
Title: TBA
Abstract: TBA
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Geometry and Topology on 22 October 2026 at 13:30 in B3.02
Speaker: Laura Wakelin (King's College London)
Title: Constructing Lagrangians in symplectic toric 4-manifolds from multi-grid diagrams
Abstract: Triple grid diagrams were introduced by Blackwell, Gay and Lambert-Cole as a way to construct Lagrangians in CP2 through the lens of an underlying trisection. We generalise this to multi-grid diagrams, which can be used to construct Lagrangians in all symplectic toric 4-manifolds. We give examples of multi-grid diagrams for a range of Lagrangians in S2 x S2, including Evans’ recent non-squeezable Klein bottle. This is joint work with Shintaro Fushida-Hardy.
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Analysis on 22 October 2026 at 16:00 in B3.02
Speaker: Dario Trevisan (University of Pisa)
Title: Wide Neural Networks: Gaussian Limits and Beyond
Abstract: Wide neural networks provide an interesting meeting point
between probability theory, analysis, and modern machine learning. As
their width tends to infinity, randomly initialized networks converge to
Gaussian processes, suggesting a relatively simple description of an
otherwise highly nonlinear random system. But how accurate is this
approximation, and what does it miss?
In this talk, I will discuss some recent mathematical results addressing
these questions. Starting from Gaussian process limits and quantitative
estimates based on optimal transport, we will explore the
large-deviation regime, where atypical fluctuations reveal a richer,
non-Gaussian structure governed by variational problems involving the
internal kernels of the network.
We will also see how these two probabilistic regimes lead to different
descriptions of Bayesian neural networks: quantitative convergence to
Gaussian process posteriors on the one hand, and large-deviation
principles that capture the interplay between prior probabilities and
observations on the other. -
Applied Mathematics on 23 October 2026 at 12:00 in B3.02
Speaker: Erik Jansson (University of Cambridge)
Title: Template deformation methods for reconstruction
Abstract: In difficult imaging regimes, incorporating prior information can drastically improve reconstructions. One approach is to require that the reconstruction is a deformation of some known prior object. In cryo-EM reconstruction of a known protein, for instance, it is reasonable to assume the reconstructed conformation is a modification of a deposited known one. In sparse limited-angle tomography, one can require that the reconstruction is a deformation of an earlier high-quality scan.
Mathematically this is a natural setting for shape analysis, where Lie groups act on shape spaces of deformable objects. Originally developed for registration, these tools can be adapted for inverse problems. In this talk I show how the same mathematical construction yields methods applicable in both cryo-EM and tomographic reconstruction. I also outline paths to bring these methods to real data, including learning-based deformation approaches. -
Combinatorics on 23 October 2026 at 14:00 in B3.02
Speaker: Lu-Ming Zhang (LSE)
Title: A Chvatal-type codegree condition for Hamiltonian cycles in k-uniform hypergraphs
Abstract: We prove an asymptotic Chvatal-type codegree criterion for tight Hamiltonian cycles in k-uniform hypergraphs for every fixed k≥3. The criterion allows small degrees to be compensated by large degrees in the link graphs of (k−2)-tuples. It strengthens the celebrated asymptotic Dirac-type theorem by Rodl, Rucinski and Szemeredi and implies, as a corollary, a Posa-type criterion conjectured by Schulke.
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Number Theory on 26 October 2026 at 15:00 in B3.02
Speaker: Hanneke Wiersema (University of Cambridge)
Title: TBA
Abstract: TBA
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Algebraic Geometry on 28 October 2026 at 15:00 in B3.02
Speaker: Fatemeh Rezaee (University of Cambridge)
Title: TBA
Abstract: TBA
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Geometry and Topology on 29 October 2026 at 13:30 in B3.02
Speaker: Dawid Kielak (University of Oxford)
Title: Fibring of Poincare-duality groups
Abstract: I will introduce Pincare-duality groups, and talk about what we know about their virtual fibring properties.
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Algebraic Geometry on 04 November 2026 at 15:00 in B3.02
Speaker: Nikon Kurnosov (UCL)
Title: TBA
Abstract: TBA
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Geometry and Topology on 05 November 2026 at 13:30 in B3.02
Speaker: Danielle West (Tel Aviv University)
Title: TBA
Abstract: TBA
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Geometry and Topology on 12 November 2026 at 13:30 in B3.02
Speaker: Koji Fujiwara (Kyoto University)
Title: TBA
Abstract: TBA
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Number Theory on 16 November 2026 at 15:00 in B3.02
Speaker: Jef Laga (University of Cambridge)
Title: TBA
Abstract: TBA
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Algebraic Geometry on 18 November 2026 at 15:00 in B3.02
Speaker: Matthew Habermann (Imperial)
Title: TBA
Abstract: TBA
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Geometry and Topology on 19 November 2026 at 13:30 in B3.02
Speaker: Giovanni Sartori (Heriot-Watt University)
Title: TBA
Abstract: TBA
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Combinatorics on 20 November 2026 at 14:00 in B3.02
Speaker: Kohki Sakamoto (Tokyo)
Title: Continuity of drift on lamplighter groups
Abstract: Lamplighter groups are classical examples in geometric group theory, with a simple interpretation in terms of a lamplighter walking around a graph and switching lamps on and off. Under this interpretation, the standard word metrics on these groups can be described in terms of the travelling salesman problem on the graph. In this talk, we will consider random walks on lamplighter groups over Z^d with d≧3, and show that the asymptotic speed is continuous as a function of the driving measure. This is joint work with Eduardo Silva.
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Algebraic Geometry on 25 November 2026 at 15:00 in B3.02
Speaker: Pierrick Bousseau (University of Oxford)
Title: TBA
Abstract: TBA
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Geometry and Topology on 26 November 2026 at 13:30 in B3.02
Speaker: Antoine Poulin (University of Warwick)
Title: TBA
Abstract: TBA
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Algebraic Geometry on 02 December 2026 at 15:00 in B3.02
Speaker: Alexia Corradini (University of Cambridge)
Title: TBA
Abstract: TBA
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Geometry and Topology on 03 December 2026 at 13:30 in B3.02
Speaker: Alexander Nolte (Institut des Hautes Études Scientifiques)
Title: TBA
Abstract: TBA
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Number Theory on 07 December 2026 at 15:00 in B3.02
Speaker: Céline Maistret (University of Bristol)
Title: TBA
Abstract: TBA
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Algebraic Geometry on 20 January 2027 at 15:00 in TBC
Speaker: Dhruv Ranganathan (University of Cambridge)
Title: TBA
Abstract: TBA
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Combinatorics on 16 October 2026 at 14:00
Speaker: Joel Moreira (Warwick)
Title: Growth rates for infinite sumsets in sets with positive density
Abstract: In 2019, in joint work with Florian Richter and Donald Robertson, we proved that any set A of natural numbers with positive upper density contains a sumset B+C where B and C are both infinite sets of natural numbers. An example of Bernard Host shows that, in general, B and C may be forced to have zero density.
There are now three or four proofs of the sumset theorem, but none of them give any growth condition on the sizes of B and C beyond Host's example. I will present ongoing joint work with Leo Verteegen, where we explore this problem. It turns out that the answer changes drastically, depending on the exact formulation of the question asked. -
Applied Mathematics on 16 October 2026 at 12:00
Speaker: Jörg Nick (University of Birmingham)
Title: The modulated Fourier expansion for waves propagating through time-modulated media
Abstract: Controlling waves by actively changing the material parameters of a medium enables the development of new acoustic and electrical devices. Modulating the material breaks classical properties like reciprocity and the conservation of energy, which complicates the mathematical analysis. Without a limiting amplitude principle, time-harmonic formulations are generally inapplicable. The talk introduces an alternative tool for the time-modulated acoustic wave equation, that is based on a modulated Fourier expansion (MFE). The solution is characterized by multiple smoothly varying coefficient functions, which solve a coupled system of evolutionary partial differential equations with temporally constant coefficients. For small-amplitude fast-time modulations, this system of evolutionary partial differential equations possesses a unique smoothly varying solution, which characterizes the exact solution up to a small defect. Discretization of the derived coupled system yields integrators that are stable and accurate when larger time steps are used, compared to those schemes that are applied to the time-modulated acoustic wave equation directly. Numerical experiments illustrate the theoretical results and the use of the approach.
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Analysis on 15 October 2026 at 16:00
Speaker: James Tissot (Imperial College London)
Title: Solutions to the Plateau Problem via Covering Spaces
Abstract: A well-known question in the calculus of variations is the Plateau problem: given a closed curve in three-dimensional space, does there exist a minimal surface spanning it? For much of its long history, the emphasis has been on finding solutions with special properties, such as prescribed genus, smoothness or orientability.
In this talk, rather than seeking a solution of a particular kind, I will describe a method aimed at producing many different solutions. The starting point is a beautiful insight of Brakke, which recasts the Plateau problem as a perimeter minimisation problem in suitable covering spaces. I will then show that, by first solving this problem in each cover and then varying the cover, one can often produce many distinct minimal surfaces spanning the boundary curve. Comparing these surfaces becomes natural, and I will show that among them there is always one of least area. Time permitting, I will discuss some elusive minimal surfaces that this approach does not (yet) capture. -
Geometry and Topology on 15 October 2026 at 13:30
Speaker: Thomas Hill (University of Warwick)
Title: Mapping class groups of infinite graphs
Abstract: The group of topological symmetries of a surface, known as the mapping class group, provides a powerful lens for studying the geometry and topology of surfaces. The outer automorphism groups of a free group, Out(\(F_n\)), can be thought of as a graph-theoretic analog of the mapping class group. Although results do not translate directly between the surface and graph settings, their structural parallels inspire questions and techniques between these areas. Over the past decade, there has been a growing interest in studying big mapping class groups, namely those of infinite-type surfaces. In this talk, I will discuss recent progress on the analog of Out(\(F_n\)) for infinite graphs, including a rigidity theorem, results about the algebraic properties of their asymptotically rigid subgroups, and recent work on actions of these groups on hyperbolic spaces, particularly obstructions to general-type actions.
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Junior Analysis and Probability on 12 October 2026 at 15:00
Speaker: Qiu Shi Wang (University of Oxford)
Title: Einstein metrics and rigorous numerics
Abstract: Einstein manifolds have been of interest to geometers for over a century. Recently, new tools were developed, combining analytical work and computational methods, to study Einstein metrics with sufficient symmetry, e.g. in the cohomogeneity one setting. In this talk, I will describe how we can use a flexible, versatile computer-assisted procedure to construct new Einstein metrics on familiar spaces such as spheres and complex projective space.
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Number Theory on 12 October 2026 at 15:00
Speaker: Ben Krause (University of Bristol)
Title: Prime Number Theory at the Interface of Harmonic Analysis and Ergodic Theory
Abstract: Prime number theory has played a central role in problems in pointwise ergodic theory, dating back to the work of Bourgain, and continuing to the present day. In this talk, we discuss some modern work in this direction, in which the operators in question incorporate an additional symmetry beyond the classical examples, and accordingly higher-order Fourier-analytic methods are required.
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Junior Algebra Seminar on 12 October 2026 at 14:00
Speaker: Jessica Anzanello (Università degli Studi di Milano-Bicocca)
Title: Fixed-point-free elements in two-orbit permutation groups
Abstract: A classical theorem of Jordan states that every non-trivial finite transitive permutation group contains a derangement, that is, an element with no fixed points. A deep result of Fein, Kantor, and Schacher adds that one can even find a derangement of prime-power order. In this talk, I will discuss a natural extension of this result to permutation groups G with two orbits on n > 2 points. In this setting, we show that either G contains a derangement, or it contains an element of prime-power order with exactly one fixed point. As a corollary, if the two orbits have size a and b, with a + b > 2 and (a, b − 1) = (a − 1, b) = 1, then G has a derangement. This confirms and generalizes a conjecture of Ellis and Harper. This is joint work with Sean Eberhard.
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Applied Mathematics on 09 October 2026 at 12:00
Speaker: David Smith (University of Birmingham)
Title: Reduced effort biological fluid mechanics
Abstract: Fluid mechanics on microscopic scales is vital to life on Earth, with examples spanning swimming marine algae and bacteria that underpin ecosystems, cilia that orient embryo development and keep organs clean, and spermatozoa that are central to many forms of sexual reproduction. These systems can often be modelled via the Stokes flow equations, which are linear, but can be complex to solve due to the presence of irregular moving boundaries. Following an introduction to the fundamental physics of microscale propulsion, this talk will describe two areas of our research: (1) methods to solve the Stokes flow equations computationally, in particular the nearest-neighbour method of regularised stokeslets -- motivated by reduction in computational 'effort' (by both the computer and the programmer!), (2) a specific physiological adaptation by which spermatozoa appear to be able to reduce the effort needed to propel themselves to the egg, which we will interpret via elastohydrodynamic computations.
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Analysis on 08 October 2026 at 16:00
Speaker: Gabriele Cassese (University of Oxford)
Title: On the homogeneous Morrey problem
Abstract: In this talk, we will describe how a connection between laminates and martingales can be used to construct examples of p-homogeneous rank-one convex integrands that are nowhere quasiconvex, answering a question of Kirchheim and Kristensen. We will also see how the method yields a homogeneous rank-one convex quartic polynomial on \mathbb{R}^{2\times3} that is nowhere quasiconvex. Together with Šverák’s 1992 result in \mathbb{R}^{3\times2}, this leaves only the 2\times2 case of Morrey’s problem open.
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Geometry and Topology on 08 October 2026 at 13:30
Speaker: Ana Isakovic (University of Cambridge)
Title: Top-dimensional \(l^2\)-homology of hyperbolic groups
Abstract: Computing \(l^2\)-homology can be a demanding task especially if one attempts to follow the definition directly. In this talk, I will speak about using automatic structures to construct top-dimensional \(l^2\)-cycles and how they can further be used to compute \(l^2\)-homology of certain hyperbolic groups.
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Algebra on 08 October 2026 at 12:00
Speaker: Ernesto Ingrosso (Napoli)
Title: Groups with dual classes of subgroups
Abstract: We completely characterize insoluble groups whose subgroups are pronormal or pronormalize every subgroup. We also completely describe p-groups with this property, and prove many structural results in the soluble case (for example, such groups are always of length at most 3 and have Sylow towers). This is joint work with M. Trombetti and A. Zitouni.
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Algebraic Geometry on 07 October 2026 at 15:00
Speaker: Paul Johnson (University of Sheffield)
Title: Betti numbers of Hilbert schemes of points on orbifold surfaces.
Abstract: Building on Ellingrud and Strømme's calculation of the Betti numbers for the Hilbert scheme of points in the plane, in his master's thesis Göttsche gave product formulas for the Betti numbers of Hilbert schemes on any smooth surface. Since a smooth DM stack should be as well behaved as a smooth surface, one should expect similar product formulas for orbifold surfaces. Indeed, when G in SL_2, the components of Hilb_n([C^2/G]) are Nakajima quiver varieties, and their cohomologies assemble into representations of quantum groups. Surprisingly, not much work had been done for more general G. In joint work with Jørgen Vold Rennemo we remedy this, giving product formulas when G is abelian and some results beyond that.
In the first half (and then some) we review Ellingsrud and Strømme's calculation of the Betti numbers for the Hilbert scheme of points in the plane, explaining how this allows you to calculate the Betti numbers of Hilb [C^2/G] when G is abelian in terms of partitions, which allowed Gusein-Zade, Luengo, and Melle-Hernández to conjecture the first product formulas and for me to extend these formulas to all abelian groups. In the remaining time we sketch Jørgen's clever trick to prove them using the Crepant Resolution Conjecture. If time allows we'll touch on what we can see about the non-abelian case. -
Junior Algebra Seminar on 05 October 2026 at 14:00
Speaker: Reuben Hillyard (University of Birmingham)
Title: Homotopy Type Theory
Abstract: Proofs and constructions in (higher) category theory can be unintuitive when written ordinarily; so we reach for alternative systems of notation, such as commutative diagrams or string diagrams. (Homotopy) type theory provides another such system, in which we imagine consuming given resources to produce others. In this talk, we will motivate homotopy type theory by considering each part of the slogan "homotopy type theory is Martin-Löf dependent type theory with intensional identity types, univalence, and higher inductive types".
Click on a title to view the abstract!