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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

Algebraic Geometry

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

Affiliated Faculty: Tom Graber, Elena Mantovan, Eric RainsDinakar 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: Rupert L. Frank, Nikolai Markarov, Nets Katz, Vladamir Markovic, Eric RainsOmer Tamuz, Lu Wang

Combinatorics

Research covers combinatorial designs and matrix theory, coding theory, extremal set theory.

Affiliated Faculty: 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: Vladimir Markovic, Yi Ni, Lu Wang

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 set theory and its interactions with analysis; combinatorics, dynamical systems, and model theory.

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, Dinakar Ramakrishnan

Mathematical Physics

Research covers Schrödinger operators, random matrices.

Affiliated Faculty: Rupert L. Frank, Alexei Kitaev, Eric RainsBarry Simon

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: Sergei Gukov, Anton Kapustin, Hirosi Ooguri

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