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.
Functional Analysis, Operator Theory
Numerical analysis and Scientific computing, Optimal control of PDEs, Computational biology and high performance computing, Computational fluid dynamics.
Differential geometry, Higher category theories, Gerbes
Number theory, arithmetic algebraic geometry, elliptic curves, modular forms and Galois representations.
Partial differential equations, Theory and numerics of hyperbolic conservation laws
Hyperbolic systems of conservation laws,Asymptotic preserving schemes,Genuinely multidimensional numerical schemes,Nonlinear waves and shock waves.
Harmonic Analysis, Sampling and Reconstruction, Wavelet Analysis
Linear Algebra & Matrix Analysis
Interest: Algebraic Geometry
Complex Dynamics and Ergodic Theory
Group theory, Commutative Algebra and Homological Algebra.
Functional Analysis/Numerical Functional Analysis, Mathematical Finance/Financial Engineering, Parameter Identification in PDEs, Mathematical Biology, Machine Learning, Data Science Research
Stochastic (Geometric) Partial Differential Equations, Stochastic Analysis, Navier-Stokes Equations, Landau-Lifshitz-Gilbert equations (Ferromagnetism), Nematic Liquid Crystals
Probability Theory and Analysis including , Stochastic PDE, Stochastic Differential Equations, Differential Equations and Applications