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

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

Differential geometry, Higher category theories, Gerbes

Harmonic Analysis, Sampling and Reconstruction, Wavelet Analysis

Linear Algebra & Matrix Analysis

Finite element methods for partial differential equations

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

Interest: Algebraic Geometry

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

Elliptic PDE's, Nonlinear Analysis

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

Complex Dynamics and Ergodic Theory

I am interested in representation theory of finite dimensional algebras.

Group theory, Commutative Algebra and Homological Algebra.