Analysis & PDEs

Calculus and the theory of real and complex continuous functions are among the crowning achievements of science. The field of mathematical analysis continues the development of that theory today to give even greater power and generality. Our faculty have made large strides in advancing our techniques to analyze partial differential equations of various types to understand the nature of their solutions.

Our group in analysis investigates free boundary problems, dispersive equations, microlocal analysis with applications to differential geometry and mathematical physics (index theory).

Department Members in This Field

Faculty

Instructors & Postdocs

  • Yvonne Alama Bronsard Nonlinear dispersive PDEs, spectral analysis, integrability, wave turbulence, tree series
  • Lior Alon Mathematical physics, Fourier analysis and quasicrystals, spectral geometry on graphs.
  • Shi Chen Machine Learning, Gradient Flows and Optimization, Inverse Problems
  • Wenkui Du Geometric Analysis (geometric flows, minimal surfaces, Allen-Cahn equations)
  • Dongyeong Ko
  • Zhengjiang Lin
  • Max Lipton Minimal Surfaces, Physical Knot Theory, Dynamical Systems
  • Oren Yakir Analysis and its applications in Probability Theory and Mathematical Physics

Graduate Students*

*Only a partial list of graduate students