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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

Richard Stanley Algebraic Combinatorics

Yufei Zhao Extremal, probabilistic, and additive combinatorics

Instructors & Postdocs

Souvik Dhara Percolation, Random graphs, Phase transition, Large deviation, Graph limits

William Cole Franks

Felix Gotti

Duncan Levear Enumerative combinatorics, Digital learning

Anna Weigandt Algebraic Combinatorics, Specifically Schubert Calculus, Combinatorial Algebraic Geometry

Graduate Students*

Aaron Berger Extremal, probabilistic, and additive combinatorics

Evan Chen

Sergei Korotkikh algebraic combinatorics, integrable probability

Ashwin Sah Graph theory, random matrix theory, additive combinatorics

Mehtaab Sawhney Combinatorics, Probability

Jonathan Tidor Additive combinatorics, higher-order Fourier analysis, discrete geometry

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

*Only a partial list of graduate students