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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).

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

Andrew Lawrie Analysis, Geometric PDEs

Richard Melrose Partial Differential Equations, Differential Geometry

William Minicozzi Geometric Analysis, PDEs

Gigliola Staffilani Analysis: Dispersive Nonlinear Partial Differential Equations

Instructors & Postdocs

Lior Alon Mathematical physics, spectral geometry and analysis, quantum graphs.

Giada Franz Geometric Analysis, with a focus on Free Boundary Minimal Surface

Malo Jezequel Hyperbolic Dynamical Systems, Spectral Theory, Microlocal Analysis

Cyril Letrouit Spectral theory, Partial differential equations, Microlocal analysis, Schrödinger operators

Dominique Maldague Harmonic analysis, decoupling and restriction theory, extremization problems

Changkeun Oh Harmonic analysis, decoupling theory, restriction theory

Tristan Ozuch-Meersseman Geometric analysis

Matthew Rosenzweig nonlinear partial differential equations, mathematical physics

Jia Shi fluid dynamics and partial differential equations

Jingze Zhu Differential Geometry and Partial Differential Equations

Graduate Students*

Shrey Aryan Optimal Transport, PDEs and Harmonic Analysis

Julius Baldauf Geometric analysis

Gonzalo Cao Labora

Alex Cohen

Yuqiu Fu

Shengwen Gan Fourier analysis

Johannes Hosle

Tang-Kai Lee Differential Geometry and Partial Differential Equations

Alexander McWeeney Geometric Analysis, Analysis & PDEs, Mathematical Physics

Joshua Messing Partial Differential Equations, Differential Geometry, Functional Analysis

Ron Nissim Mathematical Physics, Integrable Systems, Stochastic Processes

Ethan Sussman

Sarah Tammen

*Only a partial list of graduate students