Monday, September 25, 2017 - 15:00 , Location: Skiles 005 , Hung Tran , Georgia , Organizer: Dan Margalit
We give "visual descriptions" of cut points and non-parabolic cut pairs in the Bowditch boundary of a relatively hyperbolic right-angled Coxeter group. We also prove necessary and sufficient conditions for a relatively hyperbolic right-angled Coxeter group whose defining graph has a planar flag complex with minimal peripheral structure to have the Sierpinski carpet or the 2-sphere as its Bowditch boundary. We apply these results to the problem of quasi-isometry classification of right-angled Coxeter groups. Additionally, we study right-angled Coxeter groups with isolated flats whose $\CAT(0)$ boundaries are Menger curve. This is a joint work with Matthew Haulmark and Hoang Thanh Nguyen.
Monday, September 18, 2017 - 13:55 , Location: Skiles 006 , Michael Landry , Yale , email@example.com , Organizer: Balazs Strenner
Let M be a closed hyperbolic 3-manifold with a fibered face \sigma of the unit ball of the Thurston norm on H_2(M). If M satisfies a certain condition related to Agol’s veering triangulations, we construct a taut branched surface in M spanning \sigma. This partially answers a 1986 question of Oertel, and extends an earlier partial answer due to Mosher. I will not assume knowledge of the Thurston norm, branched surfaces, or veering triangulations.
Monday, September 11, 2017 - 14:30 , Location: UGA Room 304 , Jeremy Van Horn-Morris and Laura Starkston , TBA , Organizer: Caitlin Leverson
Tuesday, August 22, 2017 - 11:00 , Location: Skiles 006 , Juliette Bavard , University of Chicago , Organizer: Balazs Strenner
The mapping class group of the plane minus a Cantor set naturally appears in many dynamical contexts, including group actions on surfaces, the study of groups of homeomorphisms on a Cantor set, and complex dynamics. In this talk, I will present the 'ray graph', which is a Gromov-hyperbolic graph on which this big mapping class group acts by isometries (it is an equivalent of the curve graph for this surface of infinite topological type). If time allows, I will give a description of the Gromov-boundary of the ray graph in terms of long rays in the plane minus a Cantor set. This involves joint work with Alden Walker.
Monday, August 14, 2017 - 14:11 , Location: Skiles 006 , Albert Fathi , Georgia Tech , Organizer: Dan Margalit
We will give different topological very simple statements that seem not to have been noticed, although they are of the level of Brouwer’s fixed point theorem. The main result is: Let F be a compact subset of the manifold M. Assume g:F->M is a continuous map which is the identity on the boundary (or frontier) of F, then the image g(F) contains either F or M\F.
Monday, August 7, 2017 - 14:05 , Location: Skiles Conference Room 114 , Ingrid Irmer , University of Melbourne , Organizer: Stavros Garoufalidis
Friday, July 7, 2017 - 10:30 , Location: Skiles 006 , Nick Vlamis , Michigan , Organizer: Justin Lanier
There has been a recent interest in studying surfaces of infinite type, i.e. surfaces with infinitely-generated fundamental groups. In this talk, we will focus on their mapping class groups, often called big mapping class groups. In contrast to the finite-type case, there are many open questions regarding the basic algebraic and topological properties of big mapping class groups. I will discuss several such questions and provide some answers. In particular, I will discuss automorphism groups of mapping class groups as well as relations between topological invariants of a surface and algebraic invariants of its mapping class group. The results in the talk are based on recent joint work with Priyam Patel and ongoing joint work with Javier Aramayona and Priyam Patel.
Tuesday, June 27, 2017 - 14:05 , Location: Skiles 006 , Lei Chen , University of Chicago , Organizer: Dan Margalit
I will talk about homomorphisms between surface braid groups. Firstly, we will see that any surjective homomorphism from PB_n(S) to PB_m(S) factors through a forgetful map. Secondly, we will compute the automorphism group of PB_n(S). It turns out to be the mapping class group when n>1.