Research Interests

Harmonic Analysis on Groups

         - Representation theory of finite groups

         - Finite Gelfand pairs

         - Association schemes

         - Discrete potential theory

         - Random walks on groups and graphs

         - Spectral Graph Theory

         - Representation Theory (Locally compact groups, Haar measures, compact groups)

Geometric and Combinatorial Group Theory

         - Asymptotic Group Theory (growth functions, the Grigorchuk group, the Thompson group F)

         - Amenability (Folner functions, isoperimetric functions)

         - Sofic groups

         - Surjunctive groups (Gottschalk conjecture)

  - Dehn's  decidability probles (Word Problem, Dehn's Algorithm, Subgroup Membership Problem)

         - Cellular automata on groups

         - Group algebras (Kaplansky's conjectures)

Functional Analysis

         - Amenability and means on groups

         - Operator Algebras (C*-algebras, von Neumann algebras, subfactors)

         - Representation Theory (Locally compact groups, Haar measures, compact groups)

         - Spectral Graph Theory

Ergodic Theory and Dynamical Systems

         - Ergodic theorems

         - Symbolic Dynamics and Cellular automata on groups

         - Algebraic Dynamical Systems (a la K. Schmidt)

         - Topological Dynamics; entropy

Probability Theory

         - Finite Markov chains

         - Random walks on groups and graphs

         - System Theory

Theoretical Computer Science

         - Formal languages (regular languages, linear languages, context-free languages, languages associated with groups)

         - Automata theory (finite-state automata, push-down automata, Turing machines, Mealy machines)

         - Computability and Recursion Theory

         - Cellular automata 

Logics and Model Theory

        -  First order Logic and Model Theory

        -  Second order Monadic Logic

        -  Computability