Calculus of Variations, regularity of degenerate elliptic PDEs, optimal transport, geometric measure theory.

Nonlinear partial differential equations, nonlinear functional analysis, geometric measure theory, Sobolev spaces, image processing, calculus of variations, numerical analysis, cloaking, inverse problems, control theory, and material sciences.

Mathematical physics by analytical methods, specifically spectral theory of ergodic Schrödinger operators and random matrices; homogenization theory; quantum spin systems; matrix inequalities and quantum information theory

Mathematical physics, probability, statistical mechanics, field theories, conformal symmetry, complex analysis, lattice models, exactly solvable models, neural networks.

Partial Differential Equations,mathematical physics, harmonic analysis, differential geometry.

Spectral Analysis of partial differential operators, partial differential equations, Quantum Mathematical Physics.

Analytic Number Theory, Analytic properties of Automorphic forms and their representations, Ergodic theory on arithmetic homogeneous spaces.