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.

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.

Viral glycoproteins - HIV and others

BBSome structure and function

Direction selective circuits in the retina and their adaptive properties.

Dynamic computations in retinal ganglion cells.

Mechanisms of retinal adaptation.

Information flow along the visual pathway and interpretation of retinal adaptation by higher order visual structures.

Roles of long noncoding RNAs in gene regulation

Complexity Theory: In particular: Boolean circuit complexity, arithmetic circuit complexity, communication complexity, probabilistically checkable proofs, quantum computation and communication, randomness and derandomization.