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

  • Lior Alon Mathematical physics, spectral geometry and analysis, quantum graphs.
  • Tsz Kiu Aaron Chow Differential Geometry and Partial Differential Equations
  • Marjorie Drake Analysis, Whitney-type Extension Problems, Convexity
  • Giada Franz Geometric Analysis, with a focus on Free Boundary Minimal Surface
  • Felipe Hern├índez Mathematical physics, partial differential equations, probability
  • Adam Kay Hydrodynamic Quantum Analogues
  • Max Lipton Minimal Surfaces, Physical Knot Theory, Dynamical Systems
  • Dominique Maldague Harmonic analysis, decoupling and restriction theory, extremization problems
  • Jia Shi fluid dynamics and partial differential equations
  • Jingze Zhu Differential Geometry and Partial Differential Equations

Graduate Students*

*Only a partial list of graduate students