Please contact Saul Schleimer or Robert Kropholler if you would like to speak or to suggest a speaker.
While this page is the seminar's "main page", I will attempt to also maintain an up-to-date 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. Note that no password is required; links to the zoom session for each talk are below.
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Thursday 5 October, 14:05 (UK time), B3.02 Zeeman. Raphael Zentner (Durham University) Rational homology ribbon cobordism is a partial order |
Abstract: Last year, Ian Agol proved that ribbon knot concordance is a partial order on knots; this resolves a conjecture that has been open for more than three decades. His proof is beautiful and surprisingly simple. There is an analogous notion of ribbon cobordism for closed 3-manifolds. We use Agol's method to show that this is also a partial order within the class of irreducible 3-manifolds. This is joint work with Stefan Friedl and Filip Misev. |
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Thursday 12 October, 14:05 (UK time), B3.02 Zeeman. Mark Pengitore (University of Virginia) 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. |
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Thursday 19 October, 14:05 (UK time), B3.02 Zeeman. Clément Legrand-Duchesne (University of Bordeaux) Reconfiguration of square-tiled surfaces |
Abstract: A square-tiled 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 \(S_n\). Square-tiled 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 square-tiled 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 square-tiled 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. |
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Thursday 26 October, 14:05 (UK time), B3.02 Zeeman. None |
Abstract: None |
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Thursday 2 November, 14:05 (UK time), B3.02 Zeeman. Adele Jackson (Oxford) 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 three-manifolds. 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 run-times. I will describe a programme to show that the three-manifold homeomorphism problem is in the complexity class NP, and discuss the important sub-case of Seifert fibered spaces. |
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Thursday 9 November, 14:05 (UK time), B3.02 Zeeman. Monika Kudlinska (University of Oxford) Subgroup separability in 3-manifold and free-by-cyclic 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 3-manifold \(M\) is subgroup separable if and only if \(M\) is geometric. We will discuss the problem of subgroup separability in free-by-cyclic groups by drawing a parallel between free-by-cyclic and 3-manifold groups. Time permitting, we will discuss how to extend these ideas to find non-separable subgroups in random groups. |
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Thursday 16 November, 14:05 (UK time), B3.02 Zeeman. Robert Kropholler (University of Warwick) The landscape of Dehn functions |
Abstract: The Dehn function of a finitely presented group \(G\) can be used to measure the complexity of its word problem. Specifically the Dehn function measures the minimal area required to fill loops in the Cayley graph of \(G\). There are various analogues of the Dehn function for wider classes of groups. These all correspond to fillings of different loops in the Cayley graph. I will carefully introduce the various analogues and discuss how the various Dehn functions can be used to prove interesting results. I will be particularly interested in the case of subgroups of hyperbolic groups. |
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Thursday 23 November, 14:05 (UK time), B3.02 Zeeman. Jeffrey Giansiracusa (Durham University) 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 K-theory) is E-infinity. |
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Thursday 30 November, 14:05 (UK time), B3.02 Zeeman. Cameron Gates Rudd (MPI Bonn) TBA |
Abstract: TBA |
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Thursday 7 December, 14:05 (UK time), B3.02 Zeeman. Francesco Fournier-Facio (University of Cambridge) TBA |
Abstract: TBA |