# 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*

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*

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 *

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