Research Summary
List of Publications
Lattices in topological groups. Arithmetic lattices. Number theory and algebraic structures (cyclic algebras with structure).
Spectral geometry and generalizations. Heat invariants. Spectral optimization.
Riemannian geometry and dynamics. Metrics on surfaces. Geodesic flow. Ergodic actions. Isometry groups.
Geometric groups theory. Hyperbolic groups. Group actions. Interesting examples of groups. Limit groups.
Number theory on groups. Quantitative problems on groups. Probabilistic methods. Profinite groups. Harmonic analysis on groups.
Elementary problems. Convex geometry and graph theory. Optimization problems. Algorithms.
Teichmuller theory, mapping class groups, and moduli spaces. Abelian varieties.
Representation and character varieties. Group actions on varieties. Representations induced from geometric constructions.
Hyperbolic geometry and generalizations. Associated groups. Covers of manifolds. Symmetric spaces and locally symmetric manifolds. Homogenous manifolds.