Elliptic PDE's, Nonlinear Analysis
Finite element methods for partial differential equations
Functional Analysis, Operator Theory
mathematical analysis with a functional analytic flavor and linked to classical Operator theory, Operator algebras (von Neumann algebras and C^*-algebras), Operator spaces, Geometry of Banach spaces, Ergodic theory, Harmonic analysis, Probability theory and analysis on groups. Noncommutative L_p-space is a common thread on which I often consider various problems from classical analysis. I am also interested in applications to quantum information theory and computer science.
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.
Harmonic Analysis, Sampling and Reconstruction, Time-Frequency Analysis
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.
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