Algebraic geometry: Algebraic groups, Singularity theory Geometric invariant theory

Representation theory of real and p-adic groups: Harmonic analysis on Spherical varieties, Gelfand pairs, asymptotic representation theory

Functional analysis: Distributions and generalized functions, Microlocal analysis, Topological vector spaces.

Complex and p-adic Automorphic forms and L-functions.

Quantum metrology and precision measurements

Ultra-cold ions and atoms

Quantum Computing

Ultra-cold collisions and interactions

Other:

Dark Matter detection:

Detector physics:

Fluid Dynamics and geophysical flows

Nonlinear Partial Differential Equations and Dynamical Systems

Optical nonlinearity in plasmonic nanostructures

sub-diffraction limited imaging

Quantum dot enabled photovoltaics

ultrafast dynamics of semiconductor quantum dots

Collective behavior of ants.

Information sharing in cooperative groups.

Collective decision making.

Representation theory and Lie superalgebras

Probability and geometry.

Operator theory

Harmonic analysis.

Classical analysis

Analytic theory of differential equations.

System representation theory of matrix functions.