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 recently, probability. I have worked in broad areas of PDE, which include fluid flows on manifolds, dispersive pde, and equations with fractional diffusion.
MATH 3001  Analysis 1
Primary Instructor

Spring 2021 / Fall 2021
Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.
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 4001  Analysis 2
Primary Instructor

Fall 2019
Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 5001.
MATH 4470  Partial Differential Equations
Primary Instructor

Spring 2018 / Fall 2020 / Spring 2022
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 5001  Analysis 2
Primary Instructor

Fall 2019
Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 4001.
MATH 5470  Partial Differential Equations
Primary Instructor

Spring 2018 / Fall 2020 / Spring 2022
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 / Spring 2021
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.
MATH 8234  Topics in Differential Geometry
Primary Instructor

Fall 2021
Presents advanced topics in Differential Geometry, such as index theory, partial differential equations on manifolds, exterior differential systems, and Cartan's methods.