Combinatorics concerns the study of discrete objects. It has applications to diverse areas of mathematics and science, and has played a particularly important role in the development of computer science. While it is arguably as old as counting, combinatorics has grown remarkably in the past half century alongside the rise of computers. It borrows tools from diverse areas of mathematics. Examples include the probabilistic method, which was pioneered by Paul Erdös and uses probability to prove the existence of combinatorial structures with interesting properties, algebraic methods such as in the use of algebraic geometry to solve problems in discrete geometry and extremal graph theory, and topological methods beginning with Lovász’ proof of the Kneser conjecture. A notable application in number theory is in the proof of the Green-Tao theorem that there are arbitrarily long arithmetic progressions of primes. The Stanford Mathematics department is a leader in combinatorics, with particular strengths in probabilistic combinatorics, extremal combinatorics, algebraic combinatorics, additive combinatorics, combinatorial geometry, and applications to computer science.

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### Daniel Bump

ProfessorStanford University

Mathematics

**Office:**383-U

**Address:**

450 Serra Mall

Building 380

**Phone:**(650) 723-4011

**Email:**bump@math.stanford.edu

**Website:**http://math.stanford.edu/~bump/

**Research Interests:**automorphic forms; Lie groups & representations; number theory

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Mary V. Sunseri Professor of Statistics and Mathematics

### Persi Diaconis

Mary V. Sunseri Professor of Statistics and MathematicsStanford University

Mathematics and Statistics

**Office:**383-D

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-5183

**Email:**diaconis@math.stanford.edu

**Website:**http://statweb.stanford.edu/~cgates/PERSI/index.html

**Research Interests:**probability; combinatorics; statistics; group theory

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### Jacob Fox

Professor & Director of Mathematics Research CenterStanford University

Mathematics

**Office:**384-X

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 736-6988

**Email:**jacobfox@stanford.edu

**Research Interests:**probability; number theory; combinatorics; geometry

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### Donald Knuth

Fletcher Jones Professor of Computer Science, EmeritusStanford University

Computer Science

**Website:**http://www-cs-faculty.stanford.edu/~uno/

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### Matthew Kwan

Szegö Assistant ProfessorStanford University

Mathematics

**Office:**382-J

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-2438

**Email:**mattkwan@stanford.edu

**Website:**http://web.stanford.edu/~mattkwan

**Research Interests:**combinatorics; probability

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### Frederick Manners

Szegö Assistant ProfessorStanford University

Mathematics

**Office:**382-K

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-7824

**Email:**fmanners@stanford.edu

**Research Interests:**number theory; combinatorics

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### Kannan Soundararajan

ProfessorStanford University

Mathematics

**Office:**383-W

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 723-2629

**Email:**ksound@math.stanford.edu

**Website:**http://math.stanford.edu/~ksound/

**Research Interests:**analytical number theory

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### Jan Vondrák

Associate ProfessorStanford University

Mathematics

**Office:**383-J

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

**Phone:**(650) 724-6001

**Email:**jvondrak@stanford.edu

**Website:**http://theory.stanford.edu/~jvondrak/

**Research Interests:**combinatorics

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