Analysis & Partial Differential Equations

Michael Aizenman Analysis in Mathematical Physics	Nicolas Burq Partial differential equations, scattering theory, control of PDE's
Luis A. Caffarelli Elliptic equations	Sun-Yung Alice Chang Geometric partial differential and partial differential equations in conformal geometry.
Michael Christ Fourier analysis, partial differential equations, complex analysis in several variables	Charles Fefferman Fourier analysis and related topics
Ursula Hamenstaedt Dynamical systems and Spectral theory	Nigel Higson Operator algebras, index theory, noncommutative geometry
Vaughan Jones Operator algebras, mathematical physics and low dimensional topology	Herbert Koch Partial differential equations
Izabella Laba Harmonic analysis, geometric measure theory, combinatorics and combinatorial number theory	Gilles Lebeau Microlocal analysis, control of partial differential equations, dispersive equations
László Lempert Complex Analysis and Geometry	Richard B. Melrose
Frank Merle Qualitative properties, singularity of solutions of nonlinear partial differential equations	William Minicozzi Geometric analysis, differential geometry, minimal surfaces, harmonic maps, and geometric evolution equations.
Werner Müller Geometric analysis, spectral theory, automorphic forms	Yuval Peres Probability theory and Statistical Physics, in particular random walks, potential theory, Brownian motion, percolation, Markov chain mixing rates, Ising model on graphs. Hausdorff dimension problems and analysis of Fractal sets. Ergodic Theory
Gilles Pisier Banach spaces, Operator spaces, Operator algebras, Harmonic analysis, Martingales and Non-commutative probability	Tristan Rivière Non linear PDE, geometric analysis, variational problems in physics and geometry, geometric measure theory
Igor Rodnianski Partial differential equations and Mathematical Physics	Wilhelm Schlag Linear and nonlinear dispersive equations, spectral and scattering theory, random operators, in particular Anderson localization
Sylvia Serfaty Calculus of variations, variational problems for physics, singular perturbations, Ginzburg-Landau equations, elliptic equations. Optimal control, viscosity solutions, geometric flows and optimal transportation	Yum-Tong Siu Several complex variables, geometric analysis, differential geometry and algebraic geometry
Terence Tao Harmonic analysis, time-frequency analysis, nonlinear wave equations, nonlinear dispersive equations, connections with number theory, combinatorics, geometric measure theory, and ergodic theory	Michael E. Taylor Partial differential equations
Gunther Uhlmann Inverse problems, microlocal analysis, scattering theory, equations with multiple characteristics.	András Vasy Microlocal analysis, scattering theory and wave propagation
Dan Virgil Voiculescu Operator algebras, free probability theory, random matrices.	Steve Zelditch Spectral geometry, complex geometry, mathematical physics
Maciej Zworski Partial differential equations, microlocal analysis, mathematical physics.