Arithmetic groups and their geometric properties, representation theory, number theory, hyperbolic geometry.

Degrees

PhD 2000, Novosibirsk State University. Thesis title Geometric properties of arithmetic groups in Lobachevsky spaces. Adviser: A. D. Mednykh.

MSc 1997, with honors, Novosibirsk State University. Honors thesis: Arithmetic properties of the groups of isometries generated by three involutions in H 3. Adviser: A. D. Mednykh.

BSc 1995, with honors, Novosibirsk State University. Honors thesis: Estimates for the number of automorphisms of a Riemann surface. Adviser: A. D. Mednykh.

Employment

Durham University (Durham, UK). Lecturer, since 2005.

Institute of Mathematics, Hebrew University (Jerusalem, Israel). Postdoctoral fellow, 2003–05.

Max Planck Institut für Mathematik (Bonn, Germany). Research affiliate, 2002–03.

Sobolev Institute of Mathematics (Novosibirsk, Russia). Honorable senior research fellow, since 2001.

Novosoft Inc. (http://www.novosoft.us). Lead software developer, 2000–01.

Visiting Positions

Universidad Autґonoma de Madrid (Spain), September – October 2009, visit hosted by Prof. A. Jaikin Zapirain.

University of Chicago (USA), September – October 2008, visit hosted by Prof. B. Farb.

Hebrew University (Jerusalem, Israel), June – July 2008, visit hosted by Prof. A. Lubotzky.

Erwin Schrödinger International Institute (Vienna, Austria), March 2007, visit hosted by Prof. J. Schwermer.

Max Planck Institut für Mathematik (Bonn, Germany), July – August 2006, general research visit.

IHES (Bures-Sur-Ivette, France), February – March 2004 and February 2003, general research visits.

• [1] Finite groups and hyperbolic manifolds, with Alex Lubotzky, Invent. Math. 162 (2005), 459–472.
• [2] Counting maximal arithmetic subgroups, (with an appendix by Jordan Ellenberg and Akshay Venkatesh), Duke Math. J. 140 (2007), no. 1, 1–33.
• [3] Addendum to: On volumes of arithmetic quotients of SO(1;n), Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 6 (2007), 263–268.
• [4] Finiteness of arithmetic hyperbolic reflection groups, with Ian Agol, Peter Storm and Kevin Whyte, Groups, Geometry, and Dynamics 2 (2008), 481-498.
• [5] On fields of definition of arithmetic Kleinian reflection groups, Proc. Amer. Math. Soc. 137 (2009), 1035-1038.

• University of Durham