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

Partial Differential Equations, Calculus of Variations.

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.

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

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.

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

#### Senior research fellow

Applied mathematics, nonlinear analysis, Calculus of Variations, bifurcation theory, dynamical

systems, partial differential equations, periodic and localized solutions, applications to hydro-dynamics.

systems, partial differential equations, periodic and localized solutions, applications to hydro-dynamics.