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.

High Order Data Representation, Nonlinear Model Approximation. Taylor Models, High-Order Numerical methods

Semialgebraic Complexity of functions, Signals Acquisition via non-linear model approximation

Analytic Theory of Differential Equations, Generalized Moments, Compositions

Zeroez distribution in Families of Analytic Functions

Model-based image analysis, representation, compression. Model-based search, capturing, and animation

Partial differential equations.

Mathematical economics, statistical analysis of occurrence of asthma in children.

Topological phases of matter:

Machine Learning, statistical learning, online learning, learning theory, optimization

Nonlinear waves and wave turbulence.

Theory of fluid turbulence. Fundamental aspects and applications.

Particles in random flows.

Low-dimensional interacting systems out of equilibrium.

Interferometry and dephasing with electronic and anyonic systems.

Weak measurement, weak values and foundations of quantum mechanics.

Exotic excitations in the fractional quantum Hall effect and Topological Insulators.

Edge reconstruction and edge channels in the fractional quantum Hall effect and Topological Insulators.

Physical processes in relativistic electron-positron plasma.

The theory of nonthermal radiation from compact astronomical objects (pulsars, white dwarfs, gamma-ray bursters etc.).

Physical processes in very strong magnetic fields.

Physical processes at the surface and astrophysical appearance of strange-quark-matter stars.

Hydrodynamics and high-energy physics of colliding stellar winds in binary systems.

Harmonic Analysis

Probability