Topology and Geometric Group Theory Seminars at the Ohio State University

Aug 26 - 

Aug 28-

Sep  2 -

Sep 4-

Sep 9-

Sep 11-

Sep 16-  Yu-Chan Chang (OSU)

Dehn Functions of Bestvina--Brady Groups. 

Dehn functions are quasi-isometry invariants of finitely presented groups that measure the complexity of the word problem. Dison showed that the Dehn functions of Bestvina--Brady groups are at most quartic, and Brady gave examples of Bestvina--Brady groups that realize quadratic, cubic, and quartic Dehn functions.

In this talk, I will present a complete classification of the Dehn functions of Bestvina--Brady groups. This is joint work with Jerónimo García-Mejía and Matteo Migliorini. 

Sep 18-

Sep 23- Dragomir Saric (IAS, CUNY)

Title: Infinite Riemann surfaces: the pants, the type and the quadratic differentials

Abstract: An arbitrary infinite Riemann surface can be obtained by gluing infinitely many geodesic pairs of pants along cuffs. The Fenchel-Nielsen coordinates uniquely determine the Riemann surface structure. We give several sufficient conditions on the Fenchel-Nielsen coordinates to guarantee that the geodesic flow is ergodic. In the case when the glued pants have bounded cuff lengths, the condition can be expressed in terms of a simple random walk on a graph defined by the pants decomposition. 

We also find a surprising connection between the ergodicity of the geodesic flows and the horizontal foliations of (all) finite-area holomorphic quadratic differentials on the surface. This criterion is used to complement the sufficient conditions and to study function-theoretic properties of the surface.

Sep 25-

Sep 30- Thomas Ng (Brandeis)

Random quotients preserve negative curvature

Hyperbolic groups were introduced by Gromov in the 1980s and enjoy rich subgroup and quotient structure. Generalizations including relative, hierarchical, and acylindrical hyperbolicity, further highlight the deep connections between algebraic properties and metric negative curvature.  I will describe a model for constructing generic quotients of a group using independent random walks.  I will explain why such random quotients generically preserve the aforementioned aspects of negative curvature.  This is joint work with C. Abbott, D. Berlyne, G. Mangioni, and A. Rasmussen.

Oct 2- Hyein Choi (Rice)

Quasi-isometric embeddings of Ramanujan complexes.

Euclidean buildings (a.k.a. affine buildings and Bruhat-Tits buildings) are considered as a p-adic analogue of symmetric spaces. We show that there is no quasi-isometric embedding between the symmetric space of SL(n,R) and the Euclidean building of SL(n,Q_p). Generalizing this, we distinguish Ramanujan complexes constructed by Lubotzky-Samuels-Vishne as finite quotients of Euclidean buildings of PGL(n,F_p((y))) up to quasi-isometric embeddings. These complexes serve as high dimensional expanders with fruitful applications in mathematics and computer science.

Oct 7-

Oct 9- Franco Vargas Pallete (Arizona State)

Oct 14- 

Oct 16- Autumn break

Oct 21- 

Oct 23-Mary He (University of Oklahoma)

Oct 28-  Louisa Liles (OSU)  Lecture series 1

Oct 30- Louisa Liles (OSU) Lecture series 2

Nov 4- Louisa Liles (OSU)  Lecture series 3

Nov 6-  

Nov 11- holiday

Nov 13-

Nov 18-

Nov 20- Jim Fowler

Nov 25- Elizabeth Buchanan (University of Iowa)

Nov 27- Thanksgiving

Dec 2-

Dec 4-

Dec 9- Qiuyu Ren (UC Berkeley)

Dec 11-