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