# 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, SchrÃ¶dinger 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*

Shengwen Gan
*Fourier analysis*

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*

*Only a partial list of graduate students