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.

Design Principles of mammalian tissues

Combining mathematical models and sensitive single-molecule measurements to study how single cells interact in tissues to jointly bring about physiological goals

Combining theoretical and experimental methods to discover design principles of biological circuits

Systems level analysis of gene regulation networks, with E. coli as a model system.

Systems Immunology

Evolution

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