Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Dynamics, Geometry, & Groups Seminar

Dynamics, Geometry, & Groups - Anthony Sanchez (U Washington)

Thursday, March 4th, 2021

Time: 1:30 p.m Place:

Speaker: Anthony Sanchez (University of Washington, Seattle)

Title: Gaps of saddle connection directions for some branched covers of tori.

Abstract: Holonomy vectors of translation surfaces provide a geometric generalization for higher genus surfaces of (primitive) integer lattice points. The counting and distribution properties of holonomy vectors on translation surfaces have been studied extensively. In this talk, we consider the following question: How random are the holonomy vectors of a translation surface? We motivate the gap distribution of slopes of holonomy vectors as a measure of randomness and compute the gap distribution for the class of translation surfaces given by gluing two identical tori along a slit. No prior background on translation surfaces or gap distributions will be assumed.

Dynamics, Geometry, & Groups - Idris Assani (UNC)

Wednesday, February 24th, 2021

Time: 11:30 a.m Place:

Speaker: Idris Assani (University of North Carolina at Chapel Hill)

Title: Wiener Wintner dynamical systems.

Abstract: WW dynamical systems form a class of ergodic dynamical systems that we introduced and talked about in our 2003 book "Wiener Wintner ergodic theorems". This class offers simple proof of difficult pointwise results such as the return times and the a.e. double recurrence . We will present these simple proofs in this talk.

Dynamics, Geometry, & Groups - Anthony Genevois (CNRS)

Thursday, February 11th, 2021

Time: 1:30 p.m Place:

Speaker: Anthony Genevois (Centre national de la recherche scientifique)

Title: Asymptotic geometry of lamplighters over one-ended groups.

Abstract: This talk will be dedicated to the asymptotic geometry of wreath products of the form (finite group)wr(finitely presented one-ended group). After a general introduction, I will describe and explain a complete classification of these groups up to quasi-isometry. (Joint work with R. Tessera.)

Dynamics, Geometry, & Groups - Nir Lazarovich (Technion)

Thursday, February 4th, 2021

Time: 1:30 p.m Place:

Speaker: Nir Lazarovich (Technion Israel Institute of Technology)

Title: Flexible Stability of Surface Groups.

Abstract: Roughly speaking, a finitely presented group is said to be (flexibly) stable if any approximate action of the group on a finite set is an approximation of an action. Stability is closely related to local testability (in CS), soficity of groups, and residual finiteness. In this joint work with Arie Levit and Yair Minsky, we show that surface groups are flexibly stable using the geometry of CAT(-1) spaces and a new quantitative variant of LERF.

Dynamics, Geometry, & Groups - Marcin Sabok (McGill University)

Thursday, January 28th, 2021

Time: 1:30 p.m Place:

Speaker: Marcin Sabok (McGill University)

Title: Hyperfiniteness at Gromov boundaries.

Abstract: I will discuss recent results establishing hyperfiniteness of equivalence relations induced by actions on Gromov boundaries of various hyperbolic spaces. This includes boundary actions of hyperbolic groups (joint work with T. Marquis) and actions of the mapping class group on boundaries of the arc graph and the curve graph (joint work with P. Przytycki).

Dynamics, Geometry, & Groups - Macarena Arenas (Cambridge)

Thursday, January 21st, 2021

Time: 1:30 p.m Place:

Speaker: Macarena Arenas (University of Cambridge)

Title: Linear isoperimetric functions for surfaces in hyperbolic groups.

Abstract: One of the main characterisations of word-hyperbolic groups is that they are the groups with a linear isoperimetric function. That is, for a compact 2-complex X, the hyperbolicity of its fundamental group is equivalent to the existence of a linear isoperimetric function for disc diagrams D -->X.
It is likewise known that hyperbolic groups have a linear annular isoperimetric function and a linear homological isoperimetric function. I will talk about these isoperimetric functions, and about a (previously unexplored) generalisation to all homotopy types of surface diagrams. This is joint work with Dani Wise.

Dynamics, Geometry, & Groups - Hakan Doga (SUNY Buffalo)

Thursday, January 14th, 2021

Time: 1:30 p.m Place:

Speaker: Hakan Doga (SUNY Buffalo)

Title: A Combinatorial Description of the Knot Concordance Invariant Epsilon.

Abstract: Sitting at the intersection of 4-dimensional topology and knot theory, the knot concordance group is an important object in low-dimensional topology whose structure is not yet fully explored and understood. One approach to study knot concordance is to use knot Floer homology, introduced by Ozsvath-Szabo and Rasmussen independently in early 2000s, and the invariants obtained from this theory. In this talk, I will describe the knot concordance, introduce some basic definitions of the combinatorial knot Floer homology called the "grid homology", explain our method of computing the concordance invariant epsilon and talk about some results. This is a joint work with S. Dey.

Dynamics, Geometry, & Groups - Hang Lu Su (ICMAT Madrid)

Thursday, November 26th, 2020

Time: 2:00 p.m Place:

Speaker: Hang Lu Su (ICMAT Madrid)

Title: Left-orderable groups and formal languages.

Abstract: I will introduce the notions of left-orderable groups, the topology on the space of left-orders, and formal language complexity with respect to the Chomsky hierarchy. I will give an idea of why it is intriguing to study left-orders using language complexity by introducing a toy example with the Klein bottle group. Finally, I will introduce some recent results concerning the closure properties of positive cone complexity. This work is joint with Yago Antolín and Cristóbal Rivas.

Dynamics, Geometry, & Groups - Elia Fioravanti

Thursday, November 19th, 2020

Time: 2:00 p.m Place:

Speaker: Elia Fioravanti (Max Planck Institute for Mathematics and at the University of Bonn)

Title: Coarse-median preserving automorphisms of special groups.

Abstract: We introduce the class of "coarse-median preserving" automorphisms of coarse median groups. For instance, we show that automorphisms of right-angled Artin groups are coarse-median preserving if and only if they are untwisted (in the sense of Charney-Stambaugh-Vogtmann), while all automorphisms of hyperbolic groups are coarse-median preserving. Our main result is that, for every special group G (in the sense of Haglund-Wise), every infinite-order, coarse-median preserving outer automorphism of G can be realised as a homothety of a finite-rank median space X equipped with a ``moderate'', isometric G-action. This generalises Paulin's result that every infinite-order outer automorphism of a hyperbolic group G can be realised as a homothety of a real tree equipped with a small, isometric G-action."]

Dynamics, Geometry, & Groups - Lei Chen (Caltech)

Thursday, November 12th, 2020

Time: 2:00 p.m Place:

Speaker: Lei Chen (California Institute of Technology)

Title: Nielsen realization problem for the mapping class group.

Abstract: Nielsen realization problem for the mapping class group Mod(Sg) asks whether the natural projection pg:Homeo+(Sg)→Mod(Sg) has a section. Moreover, we also care about the realization of subgroups of Mod(S_g). In this talk, I will explain some ideas towards this problem. It will use some rotation number results and fixed points theory.