Elliptic PDE's, Nonlinear Analysis
Finite element methods for partial differential equations
Analytic aspects of algebraic numbers and Sieve methods
Functional Analysis, Operator Theory
Commutative Algebra
Partial differential equations, Theory and numerics of hyperbolic conservation laws
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.
Numerical analysis and Scientific computing, Optimal control of PDEs, Computational biology and high performance computing, Computational fluid dynamics.
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.
Harmonic Analysis, Sampling and Reconstruction, Time-Frequency Analysis
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.
Functional Analysis/Numerical Functional Analysis, Mathematical Finance/Financial Engineering, Parameter Identification in PDEs, Mathematical Biology, Machine Learning, Data Science Research
Probability Theory and Analysis including , Stochastic PDE, Stochastic Differential Equations, Differential Equations and Applications
Data Science
Applied Mathematics
Data Analytics