Ilya Gekhtman





I am an NSF postdoc in the mathematics department of Yale University until June 2018.
From July-December 2018 I will participate in the thematic semester on Teichmueller Theory at the Fields Institute in Toronto, and in Spring 2019 I will be a postdoc at the University of Toronto.
My research interests are at the nexus of ergodic theory, probability, geometric group theory, and hyperbolic geometry.
Specifically I am interested in random walks on hyperbolic groups and their relatives,  asymptotic counting problems in group theory and geometry, Patterson-Sullivan theory, Teichmueller dynamics, and dynamics in negative curvature. 
In 2015-2016 I was a postdoc at the Hausdorff Center for Mathematics in Bonn, working with Prof. Ursula Hamenstaedt and supported by her ERC Advanced Grant "Moduli."
I received a Ph.D from the University of Chicago, where my advisor was Alex Eskin.

Email: ilyagekh@gmail.com
           ilya.gekhtman@yale.edu

Papers


Dynamics of convex cocompact subgroups of mapping class groups, under revision for Geometry and Topology.

https://arxiv.org/abs/1204.1741


Stable type of the mapping class group, preprint.

https://arxiv.org/abs/1310.5364


Counting loxodromics for hyperbolic actions (with Samuel Taylor and Giulio Tiozzo), accepted, Journal of Topology.

https://arxiv.org/abs/1605.02103


Exponential torsion growth for random 3 manifolds (with Hyungryul Baik, David Bauer, Ursula Hamenstaedt, Sebastien Hensel, Thorben Kastenholtz, Bram Petri, and Daniel Valenzuela).

Online published in Int. Math. Res. Not. IMRN. doi: 10.1093/imrn/rnx076.

Also available at:

https://arxiv.org/abs/1607.00631


The smallest positive eigenvalue of fibered hyperbolic 3-manifolds (with Hyungryul Baik and Ursula Hamenstaedt), submitted.

https://arxiv.org/abs/1608.07609


Martin boundary covers Floyd boundary (with Victor Gerasimov, Leonid Potyagailo, and Wenyuan Yang), submitted.

https://arxiv.org/abs/1708.02133


Equidistribution of closed geodesics in negatively curved spaces along random walk trajectories with respect to the harmonic invariant measure, preprint.

https://arxiv.org/abs/1711.04985


Martin boundary of relatively hyperbolic groups with abelian parabolic subgroups (with Mathieu Dussaule, Victor Gerasimov and Leonid Potyagailo), submitted.
https://arxiv.org/abs/1711.11307


Counting problems in graph products and relatively hyperbolic groups (with Samuel Taylor and Giulio Tiozzo), submitted.

https://arxiv.org/abs/1711.04177


Critical exponents of invariant random subgroups in negative curvature (with Arie Levit), preprint.

https://arxiv.org/abs/1804.02995


Personal
I was born in Kiev, Ukraine, but grew up in northern Indiana, where I graduated from Penn High School
I then attended Caltech in Pasadena, California.
I am married to Galyna Dobrovolska.
I support this Statement of Inclusiveness