Seminars and Colloquia by Series

Taut branched surfaces from veering triangulations

Series
Geometry Topology Seminar
Time
Monday, September 18, 2017 - 13:55 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael LandryYale
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.

Around a big mapping class group

Series
Geometry Topology Seminar
Time
Tuesday, August 22, 2017 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Juliette BavardUniversity of Chicago
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.

Did you say Brouwer?

Series
Geometry Topology Seminar
Time
Monday, August 14, 2017 - 14:11 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Albert FathiGeorgia Tech
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.

Algebraic and topological properties of big mapping class groups

Series
Geometry Topology Seminar
Time
Friday, July 7, 2017 - 10:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nick VlamisMichigan
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.

Surjective homomorphism between surface braid groups

Series
Geometry Topology Seminar
Time
Tuesday, June 27, 2017 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lei ChenUniversity of Chicago
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.

Experimental statistics of veering triangulations.

Series
Geometry Topology Seminar
Time
Friday, June 23, 2017 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
William WordenTemple University
Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. We present experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. We will begin by discussing essential background material, including hyperbolic manifolds and ideal triangulations, and more particularly fibered hyperbolic manifolds and the construction of the veering triangulation.

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