Ilya Gekhtman




I am currently a postdoctoral fellow at the Fields Institute and the University of Toronto, working with Prof. Giulio Tiozzo.
Before that I was an NSF postdoc/Gibbs Assistant Professor at Yale University.
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."
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. 

I received my Ph.D in 2014 from the University of Chicago, where my advisor was Alex Eskin.

Email: ilyagekh@gmail.com
         

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). J. Topol. 11 (2018), no. 2, 379-419.

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), accepted, GAFA.

https://arxiv.org/abs/1804.02995


A central limit theorem for random closed geodesics: proof of the Chas–Li–Maskit conjecture (with Samuel Taylor and Giulio Tiozzo), preprint.

https://arxiv.org/abs/1711.04177


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