Combinatorics and Discrete Geometry

Combinatorics is the study of finite structures, many of which arise in other branches of mathematics or from problems arising in science or engineering. The study of combinatorics involves general questions of enumeration and structure, matroid theory and aspects of graph theory, partially ordered sets, set partitions and permutations and combinatorial structures such as finite geometries and designs. Techniques tend to be algebraic and topological, involving methods from commutative ring theory, algebraic topology, representation theory and Hopf algebras.

Discrete geometry is concerned with properties of finitely generated geometric objects such as polytopes and polyhedra, triangulations and polyhedral complexes, configurations of lines and, more generally, hyperplanes in Euclidean and other spaces, the theory of rigid and flexible frameworks, tilings and packings. Many problems in discrete geometry arise from questions in computational geometry related to algorithms for analyzing discrete geometric structures.

Faculty Members

Marcelo AguiarAlgebra, combinatorics, category theory
Robert ConnellyDiscrete geometry, computational geometry and the rigidity of discrete structures
Tara HolmSymplectic geometry
Jon KleinbergNetworks and information
Robert KleinbergAlgorithms and theoretical computer science
Allen KnutsonAlgebraic geometry and algebraic combinatorics
Lionel LevineProbability and combinatorics
Karola MeszarosAlgebraic and geometric combinatorics
Edward SwartzCombinatorics, topology, geometry, and commutative algebra
Éva TardosAlgorithm design and algorithmic game theory

Emeritus and Other Faculty

Louis BilleraGeometric and algebraic combinatorics
Shiliang GaoAlgebraic combinatorics
Marie MacDonaldNumber Theory, commutative algebra, combinatorial geometry, university mathematics education

Activities and Resources:

Historically, there have been connections between combinatorics, in particular enumeration theory, and questions in probability. In recent decades, there have been close connections between certain areas of combinatorics and questions arising in theoretical computer science and discrete optimization. Even more recently, there have arisen links to biology, in particular, the study of phylogenetics.

The group at Cornell is particularly interested in algebraic and topological combinatorics, questions of enumeration in polytopes and, more generally, matroids, combinatorial Hopf algebras and rigidity in discrete geometric structures.

Related people

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Portia Anderson

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Louis Billera

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Ahmed Bou-Rabee

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Andrew Chen

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Moriah Elkin

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Joseph Fluegemann

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Christian Gaetz

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Raj Gandhi

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Elena Hafner

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Tara Holm

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Yibo Ji

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Robert Kleinberg

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Jon M. Kleinberg

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Robert Kleinberg

Associate Professor

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Jon M. Kleinberg

Tisch University Professor of Computer Science and Information Science and Interim Dean of Computing and Information Science

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Allen Knutson

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Lionel Levine

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Yichen Ma

Ph.D. Candidate

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Marie MacDonald

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Karola Mészáros

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Luis Perez

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Edward Swartz

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Éva Tardos

Jacob Gould Schurman Professor

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Éva Tardos

Jacob Gould Schurman Professor

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Gabriel Udell

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Alexander Vidinas

Ph.D. Candidate

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Prairie Wentworth-Nice

Ph.D. Candidate

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John Whelan

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Fiona Young

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Joy Zhang

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All research areas

Algebra    Analysis    Applied Mathematics    Combinatorics and Discrete Geometry    Geometry    Logic    Probability and Statistics    Topology   
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