Hyperbolic systems of conservation laws,Asymptotic preserving schemes,Genuinely multidimensional numerical schemes,Nonlinear waves and shock waves.
Differential geometry, Higher category theories, Gerbes
Harmonic Analysis, Sampling and Reconstruction, Wavelet Analysis
Linear Algebra & Matrix Analysis
Number theory, arithmetic algebraic geometry, elliptic curves, modular forms and Galois representations.
Stochastic (Geometric) Partial Differential Equations, Stochastic Analysis, Navier-Stokes Equations, Landau-Lifshitz-Gilbert equations (Ferromagnetism), Nematic Liquid Crystals
Analysis on Graphs, Spectral Graph Theory
Operator theory, operator algebra, non commutative dynamics.
Interest: Algebraic Geometry
Functional Analysis/Numerical Functional Analysis, Mathematical Finance/Financial Engineering, Parameter Identification in PDEs, Mathematical Biology, Machine Learning, Data Science Research
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.