Martin Kassabov

Professor of Mathematics

590 Malott Hall

(607) 255-6868

Ph.D. (2003) Yale University

Research Area

Combinatorial group theory

My research interests fall into two main categories: (1) representation theory of discrete groups, mainly Kazhdan property and property tau; (2) combinatorial algebra — applications of different combinatorial methods in abstract algebra.

The main part of my research is related to properties T and tau. These properties arise from the representation theory, and they have many applications in combinatorics.

Another part of my research can be broadly described as combinatorial algebra. My research interests are concentrated in the following topics: automorphism groups, Golod-Shafarevich groups, group rings.

Selected Publications

Kazhdan constants for SL_n(Z), International Journal of Algebra and Computation (to appear). arXiv:math.GR/0311487

Symmetric groups and expanders (announcement), Electronic Research Announcements of AMS (to appear). arXiv:math.GR/0503204

Diameters of Cayley graphs of SL_n(Z/kZ) (with Tim Riley), preprint January 2005. arXiv:math.GR/0502221

Universal lattices and property Tau (with N. Nikolov), preprint February 2005. arXiv:math.GR/0502112

Universal lattices and unbounded rank expanders, preprint February 2005. arXiv:math.GR/0502237

Symmetric groups and expanders, preprint May 2005.