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

Stanford, CA 94305-2125

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

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

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

**Research Interests:**Automorphic forms Lie groups & representations Number theory

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Professor of Mathematics and Professor of Statistics

### Sourav Chatterjee

Professor of Mathematics and Professor of StatisticsStanford University

Mathematics & Statistics

**Office:**Sequoia Hall 108

**Address:**

Sequoia Hall 108

390 Serra Mall

Stanford, CA 94305-4065

**Phone:**(650) 497-3652

**Email:**souravc AT stanford.edu

**Website:**http://statistics.stanford.edu/~souravc/

**Research Interests:**Probability Theory

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Marjorie Mhoon Fair Professor in Quantitative Science; Professor (Mathematics & Statistics and, by courtesy, Electrical Enginerring)

### Amir Dembo

Marjorie Mhoon Fair Professor in Quantitative Science; Professor (Mathematics & Statistics and, by courtesy, Electrical Enginerring)Stanford University

Mathematics and Statistics

**Office:**383-C

**Address:**

450 Serra Mall

Bldg. 380

Stanford, CA 94305-2125

**Phone:**(650) 723-1851

**Email:**amir AT math.stanford.edu

**Website:**http://statweb.stanford.edu/~adembo/

**Research Interests:**

Probability theory

Stochastic processes

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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

Bldg. 380

Stanford, CA 94305-2125

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

**Email:**diaconis AT 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

ProfessorStanford University

Mathematics

**Office:**384-X

**Address:**

450 Serra Mall

Building 380

Stanford, CA 94305-2125

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

**Email:**jacobfox AT stanford.edu

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Paul Pigott Professor in the School of Engineering and Professor, by courtesy, of Electrical Engineering

### Leonidas Guibas

Paul Pigott Professor in the School of Engineering and Professor, by courtesy, of Electrical EngineeringStanford University

Computer Science

**Website:**http://geometry.stanford.edu/member/guibas/

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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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### 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 AT stanford.edu

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### Kannan Soundararajan

ProfessorStanford University

Mathematics

**Office:**383-W

**Address:**

450 Serra Mall

Bldg. 380

Stanford, CA 94305-2125

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

**Email:**ksound AT 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 AT stanford.edu

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

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