Mathematics Logo

Combinatorics

Combinatorics involves the general study of discrete objects. Reasoning about such objects occurs throughout mathematics and science. For example, major biological problems involving decoding the genome and phylogenetic trees are largely combinatorial. Researchers in quantum gravity have developed deep combinatorial methods to evaluate integrals, and many problems in statistical mechanics are discretized into combinatorial problems. Three of the four 2006 Fields Medals were awarded for work closely related to combinatorics: Okounkov's work on random matrices and Kontsevich's conjecture, Tao's work on primes in arithmetic progression, and Werner's work on percolation.

Our department has been on the leading edge of combinatorics for the last forty years. The late Gian-Carlo Rota is regarded as the founding father of modern enumerative/algebraic combinatorics, transforming it from a bag of ad hoc tricks to a deep, unified subject with important connections to other areas of mathematics. Our department has been the nexus for developing connections between combinatorics, commutative algebra, algebraic geometry, and representation theory that have led to the solution of major long-standing problems. We are also a leader in extremal, probabilistic, and algorithmic combinatorics, which have close ties to other areas including computer science.

Faculty

Daniel Kleitman Combinatorics, Operations Research

Dor Minzer

Elchanan Mossel Probability, Algorithms and Inference

Alexander Postnikov Algebraic Combinatorics

Lisa Sauermann Extremal and Probabilistic Combinatorics

Richard Stanley Algebraic Combinatorics

Yufei Zhao Extremal, probabilistic, and additive combinatorics

Instructors & Postdocs

Colin Defant Algebraic, enumerative, geometric, and dynamical combinatorics

Felix Gotti

Pakawut Jiradilok Algebraic Combinatorics, Asymptotic Combinatorics, Combinatorial Inequalities, Probability, Statistics

Melissa Sherman-Bennett cluster algebras, total positivity, combinatorics of scattering amplitudes, algebraic combinatorics

Foster Tom Algebraic combinatorics, symmetric functions, Schur-positivity

Anna Weigandt Algebraic Combinatorics, Schubert Calculus, Combinatorial Algebraic Geometry

Graduate Students*

Aaron Berger Extremal, probabilistic, and additive combinatorics

Elisabeth Bullock Combinatorics

Evan Chen Number theory, combinatorics

Sergei Korotkikh algebraic combinatorics, integrable probability

Nitya Mani

Ashwin Sah Graph theory, random matrix theory, additive combinatorics

Mehtaab Sawhney Combinatorics, Probability

Roger Van Peski Integrable probability, algebraic combinatorics, random matrix theory

*Only a partial list of graduate students