**Alexander Goncharov**,

**Ph.D., (USSR). European Mathematical Society Prize.**Arithmetic Algebraic Geometry: polylogarithms, zeta-functions, periods, Hodge theory, motives, motivic Galois groups, Quantum geometry of moduli spaces, Representation Theory and Mathematical Physics

**Students:**

Kolya Malkin

Oleksii Kislinskyi

**Andrew Casson**,

**Cambridge University, 1969. Royal Society Fellow.**Low-dimensional topology, four manifold theory, algebraic topology, hyperbolic geometry.

**Gregory Margulis**,

**Ph.D., Moscow, 1970. American Academy of Arts and Sciences. National Academy of Sciences. Fields Medal.**Lie group theory, ergodic theory, number theory, network theory, and dynamics.

**Students:**

Thomas Hille - Website

**Gregg Zuckerman**,

**Ph.D., Princeton, 1975.**Representation theory, applications of Lie theory, mathematical physics.

**Hee Oh**,

**Ph.D., Yale, 1997. Satter Prize.**Homogeneous dynamics, discrete subgroups of Lie groups, Kleinian groups, hyperbolic geometry, and the resulting applications of number theory.

**Students:**

Min Ju Lee

Pratyush Sarkar

**Igor Frenkel**,

**Ph.D., Yale, 1980. American Academy of Arts and Sciences.**Infinite-dimensional algebras, representation theory, applications of Lie theory, mathematical physics.

**Students:**

Gabriel Bergeron-Legros

**Peter Jones**,

**Ph.D., UCLA, 1978. American Academy of Arts and Sciences. National Academy of Sciences. Salem Prize.**Real, complex, and Fourier analysis, singular integrals, potential theory, dynamical systems.

**Ronald Coifman**,

**Ph.D., Geneva, 1965. Philips Professor of Mathematics, National Academy of Sciences, American Academy of Arts and Sciences, National Medal of Science, Rolf Schock prize .**Nonlinear analysis, Scattering theory, Real and complex analysis, Singular integrals, Numerical analysis, Harmonic analysis and Geometry in high dimension Data Analysis

**Students:**

James Garritano

Jennifer Laine

**Stefan Steinerberger**,

**Ph.D., Bonn, 2013.**Real, Complex and Harmonic Analysis, Spectral Theory, Partial Differential Equations, Analytic Number Theory and Applications.

**Students:**

Louis Brown

**Van Vu**,

**Ph.D., Yale, 1998. Polya Prize. Fulkerson Prize.**Combinatorics, probability, additive number theory, data science.

**Students:**

Byungmin So

**Vladimir Rokhlin**,

**Ph.D., Rice, 1983. National Academy of Sciences.**Numerical scattering theory, elliptic partial differential equations, numerical solution of integral equations.

**Wilhelm Schlag**,

**Ph.D., Caltech 1996.**Spectral Theory, Partial differential evolution equations, harmonic analysis

**Yair Minsky**,

**Ph.D., Princeton University, 1989.**Kleinian groups, Teichmuller theory, geometric group theory, holomorphic dynamics, differential geometry.

**Students:**

**Yifeng Liu**,

**Ph.D., Columbia University, 2012.**Algebraic number theory, algebraic and arithmetic geometry, automorphic forms

**Students:**

Elad Zelingher - Website