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
- Tobias Holck Colding Differential Geometry, Partial Differential Equations
- Tristan Collins Geometric Analysis, PDEs
- Semyon Dyatlov Quantum chaos, microlocal analysis, dynamical systems, scattering theory
- Larry Guth Metric geometry, harmonic analysis, extremal combinatorics
- David Jerison Partial Differential Equations, Fourier Analysis
- Christoph Kehle Analysis, Partial Differential Equations, General Relativity
- Andrew Lawrie Analysis, Geometric PDEs
- Aleksandr Logunov Harmonic Analysis, Geometrical Analysis, Complex Analysis, PDE, Nodal Geometry
- Richard Melrose Partial Differential Equations, Differential Geometry
- William Minicozzi Geometric Analysis, PDEs
- Tristan Ozuch-Meersseman Geometric analysis
- Gigliola Staffilani Analysis: Dispersive Nonlinear Partial Differential Equations
- Daniel Stroock Probability, Stochastic Analysis
Instructors & Postdocs
- Lior Alon Mathematical physics, spectral geometry, analysis on graphs, quantum graphs.
- Shi Chen Machine Learning, Gradient Flows and Optimization, Inverse Problems
- Tsz Kiu Aaron Chow Differential Geometry and Partial Differential Equations
- Marjorie Drake Analysis, Whitney-type Extension Problems, Convexity
- Wenkui Du geometric flows, minimal surfaces, Allen-Cahn equations
- Giada Franz Geometric Analysis
- Felipe Hernández Mathematical physics, partial differential equations, probability
- Zhengjiang Lin
- Max Lipton Minimal Surfaces, Physical Knot Theory, Dynamical Systems
- Jia Shi fluid dynamics and partial differential equations
- Jingze Zhu Differential Geometry and Partial Differential Equations
Graduate Students*
- Shrey Aryan Geometric Analysis, PDEs and Optimal Transport
- Alex Cohen Harmonic analysis
- Charlie Cowen-Breen PDE, machine learning, computer-assisted proofs
- Benjy Firester Geometric analysis, PDEs
- Johannes Hosle
- Yiqi Huang
- Alain Kangabire
- Elena Kim Microlocal Analysis
- Michael Law
- Tang-Kai Lee Differential Geometry and Partial Differential Equations
- Zhenhao Li
- Alexander McWeeney Geometric Analysis, Analysis & PDEs
- Joshua Messing Partial Differential Equations, Differential Geometry, Functional Analysis
- Ron Nissim Mathematical Physics, Probability, PDEs
- Xinrui Zhao RCD Spaces, Geometric Flows
*Only a partial list of graduate students