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.
Geometric groups theory. Hyperbolic
groups. Group actions. Interesting examples of 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.