Time: 10:30 a.m Place: Jeffery Hall 422
Speaker: Jing Tao (University of Oklahoma/Fields Institute)
Title: Big Torelli groups
Abstract: I will discuss some joint work with Aramayona, Ghaswala, Kent, McLeay, and Winarski on the Torelli subgroup of big mapping class groups.
Time: 10:30 a.m Place: Jeffery Hall 422
Speaker: Francesco Cellarosi (Queen's University)
Title: Central Limit Theorem via spectral method
Abstract: I will explain the Nagaev-Guivarc'h method to obtain a Central Limit Theorem for sequences of random variables coming from a large class of 1-dimensional dynamical systems, namely uniformly expanding maps of the interval. The idea is work in a suitable Banach space to establish a spectral gap for the transfer operator, and then use a perturbative argument. This talk is based on a paper by Sébastien Gouëzel.
Time: 10:30 a.m Place: Jeffery Hall 422
Speaker: Jacob Russell (CUNY)
Title: The geometry of groups via their boundaries
Abstract: Gromov revolutionized the study of finitely generated groups by purposing the study of groups as geometric objects. The success of this geometric viewpoint has inspired a whole program of classifying groups geometrically. From the geometry of the group, one can construct various boundaries; topological spaces which record the geometry of the group "at infinity". One of these boundaries, the Morse boundary, is particularly nice as the group has a natural action on it by homeomorphisms. The Morse boundary can also be equipped with a natural cross-ratio and we will discuss how the topology of the boundary coupled with this cross-ratio is actually sufficient to encode the entire geometry of the group.
Time: 10:30 a.m Place: Jeffery Hall 422
Speaker: Camille Horbez (Laboratoire de Mathématiques d’Orsay)
Title: Growth under automorphisms of hyperbolic groups
Abstract: Let G be a finitely generated group, let S be a finite generating set of G, and let f be an automorphism of G. A natural question is the following: what are the possible asymptotic behaviors for the length of f^n(g), written as a word in the generating set S, as n goes to infinity, and as g varies in the group G?
We investigate this question in the case where G is a torsion-free Gromov hyperbolic group. Growth was completely described by Thurston when G is the fundamental group of a hyperbolic surface, and can be understood from Bestvina-Handel’s work on train-tracks when G is a free group. We address the case of a general torsion-free hyperbolic group. We show in particular that every element g has a well-defined exponential growth rate under iteration of f, and that only finitely many exponential growth rates arise as g varies in G.
This is a joint work with Rémi Coulon, Arnaud Hilion and Gilbert Levitt.
Time: 10:30 am Place: Jeffery Hall 422
Speaker: Derrick Wigglesworth (Fields Institute)
Title: Groups acting on trees
Abstract: I'll discuss several of the ways one can learn about groups via their actions on trees. There will be many examples and pictures. Then, we'll briefly discuss folding paths; a tool for understanding complicated actions. Finally, I'll mention some applications of folding paths.
