Geometry and Topology
Please contact Saul Schleimer or Robert Kropholler if you would like to speak or to suggest a speaker.
We will also attempt to maintain an uptodate listing at researchseminars.org.
The seminar will be hybrid, and will be run weekly. The talk is in B3.02 Zeeman Building on Thursdays, starting at 14:05. We will open and close the Zoom session on the hour. All of the talks will be streamed at this link.

04 July 2024 at 14:00 in B3.02
Speaker: Valentina Disarlo (Heidelberg)
Title: The model theory of the curve graph
Abstract: The curve graph of a surface of finite type is a graph that encodes the combinatorics of isotopy classes of simple closed curves. It is a fundamental tool for the study of the geometric group theory of the mapping class group. In 1987 N.K. Ivanov proved that the automorphism group of the curve graph of a finite surface is the extended mapping class groups. In the following decades, many people proved analogue results for many "similar" graphs, such as the pants graph, the arc graph, etc. In response to these results, N.V. Ivanov formulated a metaconjecture. which asserts that any "natural and sufficiently rich" object associated to a surface has automorphism group isomorphic to the extended mapping class group.
We provide a model theoretical framework for Ivanov’s metaconjecture and conduct a thorough study of curve graphs from the model theoretic point of view, with particular emphasis in the problem of interpretability between different "similar" geometric complexes. In particular, we prove that the curve graph of a surface of finite type is wstable. This talk does not assume any prior knowledge in model theory.
This is joint work with Thomas Koberda (Virginia) and Javier de la Nuez Gonzalez (KIAS). 
21 June 2024 at 14:00 in B3.02
Speaker: CarlFredrik Nyberg Brodda (KIAS)
Title: TBA
Abstract: TBA

20 June 2024 at 14:00 in B3.02
Speaker: Ramon Flores (Universidad de Sevilla)
Title: Characterizing graph properties via RAAGs.
Abstract: In the last years, thorough research has been conducted in order to understand graph properties in terms of group properties of the associated rightangled Artin group (RAAG). These properties should be intrinsic, in the sense that they should not depend on a concrete system of generators of the group. In this talk, we will give a general review of the topic, with emphasis on planarity, selfcomplementarity, and existence of surjections. In particular, we will highlight the crucial role of the cohomology algebra of the group in our approach.
This is joint work with Delaram Kahrobaei (CUNY New York) and Thomas Koberda (Virginia). 
30 May 2024 at 14:00 in B3.02
Speaker: David Hume (University of Birmingham)
Title: Coarse embeddings, and yet more ways to avoid them
Abstract: Coarse embeddings (maps between metric spaces whose distortion can be controlled by some function) occur naturally in various areas of pure mathematics, most notably in topology and algebra. It may therefore come as a surprise to discover that it is not known whether there is a coarse embedding of threedimensional real hyperbolic space into the direct product of a real hyperbolic plane and a 3regular tree. One reason for this is that there are very few invariants which behave monotonically with respect to coarse embeddings, and thus could be used to obstruct coarse embeddings.
In this talk I will discuss some new invariants which combine two very classical invariants – asymptotic dimension and growth – to give different obstructions to coarse embeddings. This is joint work with John Mackay and Romain Tessera. 
23 May 2024 at 14:00 in B3.02
Speaker: Henry Segerman (Oklahoma State University)
Title: Avoiding inessential edges
Abstract: Results of Matveev, Piergallini, and Amendola show that any
two triangulations of a threemanifold with the same number of
vertices are related to each other by a sequence of local
combinatorial moves (namely, 23 and 32 moves). For some applications
however, we need our triangulations to have certain properties, for
example that all edges are essential. (An edge is inessential if both
ends are incident to a single vertex, into which the edge can be
homotoped.) We show that if the universal cover of the manifold has
infinitely many boundary components, then the set of essential ideal
triangulations is connected under 23, 32, 02, and 20 moves. Our
results have applications in veering triangulations and in quantum
invariants such as the 1loop invariant. This is joint work with Tejas
Kalelkar and Saul Schleimer. 
09 May 2024 at 14:00 in B3.02
Speaker: Rohini Ramadas (University of Warwick)
Title: Thurston theory in complex dynamics: a tropical perspective
Abstract: A rational function in one complex variable defines a branched covering from Riemann sphere CP^1 to itself. In the 1980s, William Thurston proved a theorem addressing the question: which branched coverings of the topological sphere S^2 are (suitably equivalent to) rational functions on CP^1? Thurston’s theorem is still central in onevariable complex and arithmetic dynamics.
Tropical geometry is a field in which polyhedral geometry and combinatorics are used to describe degenerations in algebraic geometry. There are connections with geometric group theory; for example, CullerVogtmann Outer Space is closely related to the space of tropical curves.
I will introduce Thurston’s theorem and describe a connection with tropical geometry. 
25 April 2024 at 14:00 in B3.02
Speaker: Nikolai Prochorov (Marseille)
Title: Thurston theory for critically fixed branched covering maps
Abstract: In the 1980’s, William Thurston obtained his celebrated characterization of rational mappings. This result laid the foundation of such a field as Thurston's theory of holomorphic maps, which has been actively developing in the last few decades. One of the most important problems in this area is the questions about characterization, which is understanding when a topological map is equivalent (in a certain dynamical sense) to a holomorphic one, and classification, which is an enumeration of all possible topological models of holomorphic maps from a given class.
In my talk, I am going to focus on the characterization and classification problems for the family of postcritically finite branched coverings, i.e., branched coverings of the 2dimensional sphere S^2 with all critical points being fixed. Maps of this family can be defined by combinatorial models based on planar embedded graphs, and it provides an elegant answer to the classification problem for this family. Further, I plan to explain how to understand whether a given critically fixed branched cover is equivalent to a critically fixed rational map of the Riemann sphere and provide an algorithm of combinatorial nature that allows us to answer this question. Finally, if time permits, I will briefly mention the connections between Thurston's theory, Teichmüller spaces and Mapping Class Groups of marked spheres.
This is a joint work with Mikhail Hlushchanka. 
14 March 2024 at 14:00 in B3.02
Speaker: Davide Spriano (University of Oxford)
Title: Uniquely geodesic groups.
Abstract: A group is uniquely geodesic (aka geodetic) if it admits a locally finite Cayley graphs where any two vertices can be connected by a unique shortest path. Despite this being a very natural geometric property, an algebraic characterization of uniquely geodetic groups has been elusive for quite some time, even for simple questions such as “are uniquely geodesic groups finitely presented”? With Elder, Gardam, Piggot and Townsend we provide the first algebraic classification of uniquely geodesic groups.

07 March 2024 at 14:00 in B3.02
Speaker: Marco Linton (University of Oxford)
Title: The coherence of onerelator groups.
Abstract: (Joint work with Andrei JaikinZapirain.) A group is said to be coherent if all of its finitely generated subgroups are finitely presented. In this talk I will sketch a proof of Baumslag’s conjecture that all onerelator groups are coherent, discussing connections with the nonpositive immersions property and the vanishing of the second L^2 Betti number.

29 February 2024 at 14:00 in B3.02
Speaker: Joe MacManus (University of Oxford)
Title: Groups quasiisometric to planar graphs
Abstract: A classic and important theorem originating in work of Mess states that a f.g. group is quasiisometric to a complete Riemannian plane if and only if it is a virtual surface group. Another related result obtained by Maillot states that a f.g. group is virtually free if and only if it is quasiisometric to a complete planar simply connected Riemannian surface with noncompact geodesic boundary. These results illustrate the general philosophy that planarity is a very `rigid' property amongst f.g. groups.
In this talk I will build on the above and sketch how to characterise those f.g. groups which are quasiisometric to planar graphs. Such groups are virtually free products of free and surface groups, and thus virtually admit a planar Cayley graph. The main technical step is proving that such a group is accessible, in the sense of Dunwoody and Wall. This is achieved through a careful study of the dynamics of quasiactions on planar graphs. 
01 February 2024 at 14:00 in B3.02
Speaker: Samuel Shepherd (Vanderbilt University)
Title: Oneended halfspaces in group splittings
Abstract: I will introduce the notion of halfspaces in group splittings and discuss the problem of when these halfspaces are oneended. I will also discuss connections to JSJ splittings of groups, and to determining whether groups are simply connected at infinity. This is joint work with Michael Mihalik.

25 January 2024 at 14:00 in B3.02
Speaker: Francesco FournierFacio (University of Cambridge)
Title: Infinite simple characteristic quotients
Abstract: The rank of a finitely generated group is the minimal size of a generating set. Several questions that received a lot of attention around 50 years ago ask about the rank of finitely generated groups, and how this relates to the rank of their direct powers. In this context, Wiegold asked about the existence of infinite simple characteristic quotients of free groups. I will review this framework, present several open questions – old and new – and present a solution to Wiegold’s problem.
Joint with Rémi Coulon 
18 January 2024 at 14:00 in B3.02
Speaker: Ian Leary (University of Southampton)
Title: Residual finiteness of generalized BestvinaBrady groups
Abstract: (joint with Vladimir Vankov)
I discovered/created generalized BestvinaBrady groups to give an uncountable family
of groups with surprising homological properties. In this talk, I will introduce the
groups and describe joint work with Vladimir Vankov addressing the following questions:
when are they virtually torsionfree?
when are they residually finite?
This leads naturally to a third question:
when do they virtually embed in rightangled Artin groups?
There are nice conjectural answers to all three questions, which we have proved in
some cases. 
11 January 2024 at 14:00 in B3.02
Speaker: Richard Wade (University of Oxford)
Title: Quasiflats in the Aut free factor complex
Abstract: We will describe families of quasiflats in the "$Aut(F_n)$ version" of the free factor complex. This shows that, unlike its more popular "Outer" cousin, the Aut free factor complex is not hyperbolic. The flats are reasonably simple to describe and are shown to be q.i. embedded via the construction of a coarse Lipschitz retraction. This leaves many open problems about the coarse geometry of this space, and I hope to talk about a few of them. This is joint work with Mladen Bestvina and Martin Bridson.

07 December 2023 at 14:00 in B3.02
Speaker: Sam Hughes (University of Oxford)
Title: Centralisers and classifying spaces for Out(F_N)
Abstract: In this talk I will outline reduction theory for mapping classes and explain various attempts to construct similar machinery for elements of Out(F_N). I will then present a new reduction theory for studying centralisers of elements in IA_3(N), the finite index level 3 congruence subgroup of Out(F_N). Using this I will explain an application to the classifying space for virtually cyclic subgroups, a space notable for its appearance in the FarrellJones Conjecture. Based on joint work with Yassine Guerch and Luis Jorge Sánchez Saldaña.

30 November 2023 at 14:00 in B3.02
Speaker: Cameron Rudd (MPIM Bonn)
Title: Stretch laminations and hyperbolic Dehn surgery
Abstract: Given a hyperbolic manifold M and a homotopy class of maps from M to the circle, there is an associated geodesic "stretch" lamination encoding at which points in M the Lipschitz constant of any map in the homotopy class must be large. Recently, FarreLandesbergMinsky related these laminations to horocycle orbit closures in infinite cyclic covers and when M is a surface, they analyzed the possible structure of these laminations. I will discuss the case where M is a 3manifold and give the first 3dimensional examples where these laminations can be identified. The argument uses the Thurston norm and tools from quantitative Dehn surgery.

23 November 2023 at 14:00 in B3.02
Speaker: Jeffrey Giansiracusa (University of Durham)
Title: Topology of the matroid Grassmannian
Abstract: The matroid Grassmannian is the moduli space of oriented matroids; this is an important combinatorial analogue of the ordinary oriented real Grassmannian. Thirty years ago MacPherson showed us that understanding the homotopy type of this space can have significant implications in manifold topology, such as providing combinatorial formulae for the Pontrjagin classes. In some easy cases, the matroid Grassmannian is homotopy equivalent to the oriented real Grassmannian, but in most cases we have no idea whether or not they are equivalent. This question is known as MacPherson's conjecture. I'll show that one of the important homotopical structures of the oriented Grassmannians has an analogue on the matroid Grassmannian: the direct sum monoidal product (which gives rise to topological Ktheory) is Einfinity.

16 November 2023 at 14:00 in B3.02
Speaker: Rob Kropholler (Warwick)
Title: The landscape of Dehn functions
Abstract: 

09 November 2023 at 14:00 in B3.02
Speaker: Monika Kudlinska (University of Oxford)
Title: Subgroup separability in 3manifold and freebycyclic groups
Abstract: A group G is said to be subgroup separable if every finitely generated subgroup of G is the intersection of finite index subgroups. It is known that a fundamental group of a compact, irreducible, closed 3manifold M is subgroup separable if and only if M is geometric. We will discuss the problem of subgroup separability in freebycyclic groups by drawing a parallel between freebycyclic and 3manifold groups. Time permitting, we will discuss how to extend these ideas to find nonseparable subgroups in random groups

02 November 2023 at 14:00 in B3.02
Speaker: Adele Jackson (University of Oxford)
Title: Algorithms for Seifert fibered spaces
Abstract: Given two mathematical objects, the most basic question is whether they are the same. We will discuss this question for triangulations of threemanifolds. In practice there is fast software to answer this question and theoretically the problem is known to be decidable. However, our understanding is limited and known theoretical algorithms could have extremely long runtimes. I will describe a programme to show that the 3manifold homeomorphism problem is in the complexity class NP, and discuss the important subcase of Seifert fibered spaces.

19 October 2023 at 14:00 in B3.02
Speaker: Clément Legrand (LaBRI)
Title: Reconfiguration of squaretiled surfaces
Abstract: A squaretiled surface is a special case of a quadrangulation of a surface, that can be encoded as a pair of permutations in \(S_n \times S_n\) that generates a transitive subgroup of \(S_n\). Squaretiled surfaces can be classified into different strata according to the total angles around their conical singularities. Among other parameters, strata fix the genus and the size of the quadrangulation. Generating a random squaretiled surface in a fixed stratum is a widely open question. We propose a Markov chain approach using "shearing moves": a natural reconfiguration operation preserving the stratum of a squaretiled surface. In a subset of strata, we prove that this Markov chain is irreducible and has diameter \(O(n^2)\), where \(n\) is the number of squares in the quadrangulation.

12 October 2023 at 14:00 in B3.02
Speaker: Mark Pengitore (University of Virginia)
Title: Residual finiteness growth functions of surface groups with respect to characteristic quotients
Abstract: Residual finiteness growth functions of groups have attracted much interest in recent years. These are functions that roughly measure the complexity of the finite quotients needed to separate particular group elements from the identity in terms of word length. In this talk, we study the growth rate of these functions adapted to finite characteristic quotients. One potential application of this result is towards linearity of the mapping class group

05 October 2023 at 14:00 in B3.02
Speaker: Raphael Zentner (Durham University)
Title: Rational homology ribbon cobordism is a partial order
Abstract: Last year, Ian Agol has proved that ribbon knot concordance is a partial order on knots, a conjecture that has been open for more than three decades. His proof is beautiful and surprisingly simple. There is an analog notion of ribbon cobordism for closed 3manifolds. We use Agol's method to show that this notion of ribbon cobordism is also a partial order within the class of irreducible 3manifolds. This is joint work with Stefan Friedl and Filip Misev.
Click on a title to view the abstract!