Authomorphic forms, representation theory, trace formula

Non-commutative ring theory, Algebras satisfying polynomial identities

Combinatorics: Symmetric functions, Permutation statistics

Circum-nuclear accretion disks

The growth of black holes in the early universe

Gravitational wave sources

Massive black holes

Dynamic of galactic nuclei

Stellar phenomena in the center of the Milky Way

Number theory.

Algebraic geometry.

Non-Archimedean analytic geometry.

Analytic theory of ordinary differential equations.

Singularity theory. Singular foliations, limit cycles, holonomy.

Breast cancer progression and metastasis.

Invariant distributions

Representation theory of reductive groups over local fields: Representations of real reductive groups, Representations of p-adic reductive groups, Relative representation theory, Gelfand pairs

Classical analysis.

Operator theory.

Inverse problems.

Combinatorics and discrete Fourier analysis.

Quantum interference phenomena in the fractional Quantum Hall effect. Electronic transport in strong magnetic fields.

Non-abelian electronic states - quantum Hall states, topological superconductors and Majorana fermions.

Fractionalized topological phases - how to construct them, how to measure them, and how to use them for topological quantum computation

Low density two dimensional electronic systems.

One dimensional electronic systems - electronic transport in the presence of interactions.