Biophysics, Computational Methods, Partial Differential Equations

Ergodic theory, probability, harmonic analysis, operator theory

Dynamical Systems and Ergodic Theory, Teaching of College Mathematics

PDEs, Semiclassical Analysis, Mathematical Physics, Quantum Mechanics, Differential Geometry

Representation Theory, Mathematical Physics, Algebraic Combinatorics, Number Theory, Algebraic Geometry...

Partial Differential Equations, Spectral Geometry, Microlocal Analysis, Quantum Chaos

Algebraic geometry, Topological Recursion, Hitchin systems

Math and statistics education, topology of 3-dimensional manifolds, mathematical modeling of disease

Computational and applied mathematics, cardiovascular physiology, fluid-structure interaction, scientific computing...

Analysis based fast algorithms, integral equations, potential theory, scientific computing, and their applications...

Numerical optimization, computational geometry and imaging, machine learning and their applications in biology and medicine.

Representation Theory

Fluid dynamics, turbulent transport

Partial differential equations, microlocal analysis

Computational simulation of multiscale, multiphysics systems. Data-driven constitutive relations for hyperelastic materials...

Applied Mathematics, Stochastic Differential Equations, Dynamical Systems

Geometry, Topology, Singularity theory

Low-dimensional topology, representation theory, homological algebra, category theory

Physical Applied Mathematics, Soft and Active Matter, Hydrodynamic Quantum Analogs, Fluid Mechanics...

Algebraic and Differential Geometry, Topology, Mathematical Physics

Partial differential equations, harmonic analysis, geometric analysis, stochastic analysis

Mathematics Education

I work in the area of partial differential equations