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
- 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
- Aleksandr Logunov Harmonic Analysis, Geometrical Analysis, Complex Analysis, PDE, Nodal Geometry
- Richard Melrose Partial Differential Equations, Differential Geometry
- William Minicozzi Geometric Analysis, PDEs
- Tomasz Mrowka Gauge Theory, Differential Geometry
- Tristan Ozuch-Meersseman Geometric analysis
- Gigliola Staffilani Analysis: Dispersive Nonlinear Partial Differential Equations
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*
- Shrey Aryan Geometric Analysis, PDEs and Optimal Transport
- Paige Bright Harmonic Analysis, Projection Theory, Fractal Geometry
- Charlie Cowen-Breen PDE, machine learning, computer-assisted proofs
- Yunchu Dai
- Benjy Firester Geometric analysis, PDEs
- Johannes Hosle
- Yiqi Huang
- Alain Kangabire
- Elena Kim Microlocal analysis, quantum chaos
- Marvin Koonce Analysis of PDE, Nonlinear Wave Equations
- Michael Law
- Zhenhao Li
- Alexander McWeeney Geometric Analysis, Analysis & PDEs
- Joshua Messing Partial Differential Equations, Differential Geometry, Functional Analysis
- Ron Nissim Mathematical Physics, Probability
- Mahnav Petersen
- Dmitrii Zakharov
*Only a partial list of graduate students