Math Research

Research in the field of mathematics covers a broad range of areas, including

Algebra

Research covers finite group theory, algebraic groups, representation theory, symmetric functions, algebraic K-theory.

Affiliated Faculty: Matthias Flach, Dinakar Ramakrishnan, Xinwen Zhu

Algebraic Geometry

Research covers moduli spaces, birational geometry, Hodge theory, Calabi-Yau varieties, arithmetic geometry.

Affiliated Faculty: Tom Graber, Elena Mantovan, Eric Rains, Dinakar Ramakrishnan, Xinwen Zhu

Analysis

Research covers classical real and complex analysis, harmonic analysis, functional analysis and operator theory, orthogonal polynomials; complex, smooth, and random dynamical and Hamiltonian systems, fractal, integrable systems, partial differential equations.

Affiliated Faculty: Nikolai Markarov, Nets Katz, Maksym Radziwill, Eric Rains, Omer Tamuz

Combinatorics

Research covers extremal and probabilistic combinatorics, additive combinatorics and Ramsey theory.

Affiliated Faculty: David Conlon, Nets Katz, Eric Rains

Geometry and Topology

Research covers low-dimensional topology, hyperbolic geometry, geometric group theory and foliations; symplectic geometry and topology, topological gauge theory, knot theory, and their interface with theoretical physics.

Affiliated Faculty: Sergei Gukov, Yi Ni

Noncommutative Geometry

Research covers noncommutative differential geometry and its applications to physics and number theory andnoncommutative algebraic geometry and the theory of noncommutattive motives.

Affiliated Faculty: Matilde Marcolli, Eric Rains

Mathematical Logic

Research covers mathematical logic and its interactions with analysis, dynamical systems and combinatorics.

Affiliated Faculty: Alexander Kechris

Number Theory

Research covers algebraic number theory, automorphic forms, Shimura varieties, Galois representations, and L-functions.

Affiliated Faculty: Matthias Flach, Elena Mantovan, Maksym Radziwill, Dinakar Ramakrishnan, Xinwen Zhu

Mathematical Physics

Research covers Schrödinger operators, random matrices.

Affiliated Faculty: Sergei Gukov, Alexei Kitaev, Eric Rains, Barry Simon

Probability

Research covers stochastic processes, statistical mechanics, random geometry, and relations to mathematical physics, complex analysis and ergodic theory.

Affiliated Faculty: Thomas Hutchcroft, Omer Tamuz, Nick Makarov

String Theory (Mathematical Aspects)

Research covers enumerative geometry, mirror symmetry, gauge theory and its applications to low-dimensional topology and the geometric representation theory.

Affiliated Faculty: Tom Graber, Sergei Gukov, Anton Kapustin, Hirosi Ooguri, Tony Yue Yu

Mathematical and Computational Linguistics

Research focuses on mathematical models of acquisition and evolution of natural languages.

Affiliated Faculty: Matilde Marcolli

Mathematical Structures in Quantum Physics

Research covers algebraic and geometric structures arising in quantum field theory, string theory, and other high-energy physics models.

Affiliated Faculty: Matilde Marcolli

Quantum Topology

Research covers various constructions of topological invariants of knots and 3-manifolds based on representation theory of quantum groups and vertex algebras.

Affiliated Faculty: Sergei Gukov