Elliptic PDE's, Nonlinear Analysis

Partial differential equations,Control theory,Game theory,Viscosity solution theory,Navier stokes equations,Image processing

Finite element methods for partial differential equations

I am interested in representation theory of finite dimensional algebras.

Analytic aspects of algebraic numbers and Sieve methods

Hyperbolic systems of conservation laws,Asymptotic preserving schemes,Genuinely multidimensional numerical schemes,Nonlinear waves and shock waves.

Functional Analysis/Numerical Functional Analysis, Mathematical Finance/Financial Engineering, Parameter Identification in PDEs, Mathematical Biology, Machine Learning, Data Science Research

Functional Analysis, Operator Theory

Commutative Algebra

Numerical analysis and Scientific computing, Optimal control of PDEs, Computational biology and high performance computing, Computational fluid dynamics.

Harmonic Analysis, Sampling and Reconstruction, Time-Frequency Analysis

Linear Algebra & Matrix Analysis

Differential geometry, Higher category theories, Gerbes

mathematical analysis with a functional analytic flavor and linked to classical Operator theory, Operator algebras (von Neumann algebras and C^*-algebras), Operator spaces, Geometry of Banach spaces, Ergodic theory, Harmonic analysis, Probability theory and analysis on groups. Noncommutative L_p-space is a common thread on which I often consider various problems from classical analysis. I am also interested in applications to quantum information theory and computer science.

Interest: Algebraic Geometry

Complex Dynamics and Ergodic Theory

Number theory, arithmetic algebraic geometry, elliptic curves, modular forms and Galois representations.

Partial differential equations, Theory and numerics of hyperbolic conservation laws

Stochastic (Geometric) Partial Differential Equations, Stochastic Analysis, Navier-Stokes Equations, Landau-Lifshitz-Gilbert equations (Ferromagnetism), Nematic Liquid Crystals

Group theory, Commutative Algebra and Homological Algebra.