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 run weekly, with one 30 minute talk, followed by a 20 minute discussion/Q&A. The talk starts five minutes after the hour. We will open and close the Zoom session on the hour. Links for each session can be found below; no password is required.
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Thursday October 7, 15:05 (UK time). Robert Kropholler (Warwick) Coarse embeddings and homological filling functions |
Abstract: The homological filling function of a finitely presented group \(G\) measures the difficulty of filling loops with surfaces in a classifying space. The behaviour of this function when passing to finitely presented subgroups is rather wild. If one adds assumptions on the dimension of \(G\), then one can bound the homological filling function of the subgroup by that of \(G\). I will discuss how to generalise these results from subgroups to coarse embeddings and also to higher dimensional filling functions. This is joint work with Mark Pengitore. |
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Thursday October 14, 15:05 (UK time). Ian Leary (Southampton) Graphical small cancellation and groups of type \(\FP\) |
Abstract: Graphical small cancellation was introduced by Gromov to embed an expanding family inside the Cayley graph of a finitely generated group. We use this technique to construct a large family of groups of type \(\FP\), most of which are not finitely presented. This is the first time non-finitely presented groups of type \(\FP\) have been constructed without using Bestvina-Brady Morse theory. I will give an idea of how graphical small cancellation works and how we use it. This is joint work with Tom Brown. |
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Thursday October 21, 15:05 (UK time). Camille Horbez (Orsay) Orbit equivalence rigidity of irreducible actions of right-angled Artin groups |
Abstract: A central goal in measured group theory is to classify free, ergodic, measure-preserving actions of countable groups on probability spaces up to orbit equivalence: that is, up to the existence of a measure space isomorphism sending orbits to orbits. Rigidity occurs when orbit equivalence of two actions forces them to be conjugate through a group isomorphism. In this talk, I will present orbit equivalence rigidity phenomena for actions of (centerless, one-ended) right-angled Artin groups, upon imposing that every standard generator acts ergodically on the space. This is joint work with Jingyin Huang. |
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Thursday October 28, 15:05 (UK time). None (None) None |
Abstract:None
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Thursday November 4, 15:05 (UK time). Rachel Skipper (Ohio) Braiding groups of homeomorphisms of Cantor sets |
Abstract: We will discuss some ways in which one can braid some classical subgroups of the homeomorphism group of the Cantor set. This includes Higman-Thompson groups and self-similar groups, as well as the topological finiteness properties of the resulting groups. The talk will include some joint work with Xiaolei Wu and Matthew Zaremsky.
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Thursday November 11, 15:05 (UK time). Benjamin Ward (BGSU) Massey Products for Graph Homology. |
Abstract: This talk is about graph complexes and their homology. A graph complex can be thought of as a generalization of a dg associative algebra, but with more sophisticated composition operations allowing for particles to collide along any graph, not just along a line. Is every graph complex quasi-isomorphic to its homology? Continuing the analogy with associative algebras the answer is no, but we will see how an A-infinity analog of graph complexes can be used to rectify this situation. We will then discuss what these higher operations can tell us in the particular cases of Lie and commutative graph homology.
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Thursday November 18, 15:05 (UK time). Sam Kim (KIAS) Optimal regularity of mapping class group actions on the circle |
Abstract: We prove that for each finite index subgroup \(H\) of the mapping class group of a closed hyperbolic surface, and for each real number \(r > 1\) there does not exist a faithful \(C^r\)-action (in the Hölder sense) of \(H\) on a circle. For this, we partially determine the optimal regularity of faithful actions by right-angled Artin groups on a circle. This is joint work with Thomas Koberda and Cristobal Rivas.
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Thursday November 25, 15:05 (UK time). Giles Gardam (Münster) The Kaplansky conjectures |
Abstract: Three conjectures on group rings of torsion-free groups are commonly attributed to Kaplansky, namely the unit, zero divisor and idempotent conjectures. For example, the zero divisor conjecture predicts that if \(K\) is a field and \(G\) is a torsion-free group, then the group ring \(K[G]\) has no zero divisors. I will discuss these conjectures and their relationship to other conjectures and properties of groups. I will then explain how modern solvers for Boolean satisfiability can be applied to them, producing the first counterexample to the unit conjecture. |
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Thursday December 2, 15:05 (UK time). Emily Stark (Wesleyan) Graphically discrete groups and rigidity |
Abstract: Rigidity theorems prove that a group's geometry determines its algebra, typically up to virtual isomorphism. Motivated by rigidity problems, we study graphically discrete groups, which impose a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds. We will present new examples, proving this property is not a quasi-isometry invariant. We will discuss action rigidity for free products of residually finite graphically discrete groups. This is joint work with Alex Margolis, Sam Shepherd, and Daniel Woodhouse. |
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Thursday December 9, 15:05 (UK time). Arnaud De Mesmay (UPEM) Short canonical decompositions of non-orientable surfaces |
Abstract: Suppose that $S$ is a surface and $G \subset S$ is an embedded graph. In many applications, during algorithm design, and even when representing the embedding, there is a basic task: to cut $S$ into a single disk. When $S$ is orientable, it has long been known how to compute a canonical cutting system that is also "short": each arc of the system runs along each edge of $G$ at most a constant number of times. In this talk we survey what is known about such cutting problems. We then explain how to obtain a short canonical system when $S$ is non-orientable. This is joint work with Niloufar Fuladi and Alfredo Hubard. |