Geometry and Topology

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.

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

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.

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.

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

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

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.

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.

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.
Seminars from 2023/2024
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