My research interests are in partial differential equations (PDE), looking from the geometrical point of view, and making connections between PDE, differential geometry, harmonic analysis, gauge theory, mathematical physics, and very recently, probability. I have worked in broad areas of PDE, which include fluid flows on manifolds, dispersive pde, and equations with fractional diffusion.
MATH 3430  Ordinary Differential Equations
Primary Instructor

Fall 2018 / Spring 2019 / Fall 2019
Involves an elementary systematic introduction to firstorder scalar differential equations, nth order linear differential equations, and ndimensional linear systems of firstorder differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.
MATH 4470  Partial Differential Equations
Primary Instructor

Spring 2018
Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Same as MATH 5470.
MATH 5470  Partial Differential Equations
Primary Instructor

Spring 2018
Studies initial boundary and eigenvalue problems for the wave, heat and potential equations. Solution by separation of variables, Green's function, and variational methods. Department enforced prerequisite: MATH 3430 or MATH 5430. Instructor consent required for undergraduates. Same as MATH 4470.
MATH 6230  Introduction to Differential Geometry 1
Primary Instructor

Spring 2020
Introduces topological and differential manifolds, vector bundles, differential forms, de Rham cohomology, integration, Riemannian metrics, connections and curvature. Department enforced prerequisites: MATH 2130 and MATH 4001. Instructor consent required for undergraduates.