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
Analysis on Graphs, Spectral Graph Theory
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.