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.

Department Members in This Field

Faculty

• Daniel Kleitman Combinatorics, Operations Research
• Dor Minzer
• Elchanan Mossel Probability, Algorithms and Inference
• Alexander Postnikov Algebraic Combinatorics
• Leonid Rybnikov Representation Theory, Integrable Systems, Quantization, Kashiwara Crystals
• Lisa Sauermann Extremal and Probabilistic Combinatorics
• Richard Stanley Algebraic Combinatorics
• Yufei Zhao Extremal, probabilistic, and additive combinatorics

Instructors & Postdocs

• Manik Dhar Combinatorics, Theoretical Computer Science
• Pakawut Jiradilok Algebraic Combinatorics, Asymptotic Combinatorics, Combinatorial Inequalities, Probability, Statistics
• Sammy Luo Extremal and additive combinatorics
• Yihui Quek Quantum Computing, Complexity Theory, Quantum Noise and Error Correction
• Melissa Sherman-Bennett cluster algebras, total positivity, combinatorics of scattering amplitudes, algebraic combinatorics
• Michael Simkin Probabilistic combinatorics, random graphs, and random processes
• Foster Tom Algebraic combinatorics, symmetric functions, Schur-positivity, chromatic symmetric functions
• Minh-Tâm Trinh

Graduate Students*

• Ilani Axelrod-Freed
• Elisabeth Bullock Combinatorics
• Evan Chen Number theory, combinatorics
• Byron Chin
• Travis Dillon
• Ryota Inagaki
• Nitya Mani
• Matthew Nicoletti Probability, Mathematical Physics
• Ashwin Sah Graph theory, random matrix theory, additive combinatorics
• Mehtaab Sawhney Combinatorics, Probability
• Oriol Sole Pi
• Yuan Yao Algebraic Combinatorics

*Only a partial list of graduate students