Partial differential equations,Control theory,Game theory,Viscosity solution theory,Navier stokes equations,Image processing
I am interested in representation theory of finite dimensional algebras.
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
Operator theory, operator algebra, non commutative dynamics.
Harmonic Analysis Sampling and Reconstruction Wavelet Analysis Applied Cryptography
Linear Algebra & Matrix Analysis
Differential geometry, Higher category theories, Gerbes
Interest: Algebraic Geometry
Complex Dynamics and Ergodic Theory
Number theory, arithmetic algebraic geometry, elliptic curves, modular forms and Galois representations.
Analysis on Graphs, Spectral Graph Theory
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.