Harmonic Analysis and Functional Analysis

We study a wide range of problems in classical and modern analysis, including spectral theory of differential operators on  manifolds, real harmonic analysis and non-smooth partial differential equations, perturbation theory, non-linear partial differential equations, special functions and their applications in  physics, operator theory and operator algebras, non-commutative geometry, abstract harmonic analysis, topological K-theory and index theory, ergodic theory and application in geometry and number theory, representations of Lie groups and analysis on symmetric and locally symmetric spaces.