Algebra and Combinatorics

Algebra refers to the use and manipulation of symbols, often with each representing some mathematical entity such as a quantity (think integer or real number), a set with special structure (think group, ring, topological space, or vector bundle) or an element of such a set, or a relation (think function, partial order, or homomorphism). Manipulation of symbols usually follows specified rules that allow for operations such as addition, multiplication, composition, or action of one object upon another. In representation theory, for example, groups act on vector spaces; and in commutative algebra, elements of rings are viewed as functions on spaces.

Combinatorics is the study of finite or discrete structures, such as networks, polyhedra, codes, or algorithms. The structures might have their origins in geometry, topology, computation, data analysis, probability, algebra, or natural sciences such as biology and physics. The overlap with algebra, for instance, is exemplified by number theory, which at its core concerns arithmetic (multiplicative or additive algebraic properties) of the integers (a countable discrete totally ordered set).

Various aspects of algebra and combinatorics are represented at Duke, from geometry to probability, from physics to computation, from statistics to topology, and everything in between.

Faculty

Michael Abel

Instructor* of Mathematics

Keywords in this area
Quantum Algebra, Categorification

Other research areas
Algebra & Combinatorics Topology

Pankaj K. Agarwal

RJR Nabisco Professor of Computer Science in Trinity College of Arts and Sciences

Robert Bryant

Philip Griffiths Professor of Mathematics

Keywords in this area
integrability, symplectic geometry

Robert Calderbank

Charles S. Sydnor Professor of Computer Science

Keywords in this area
error-correcting codes, wireless communication, data storage, discrete harmonic analysis, sphere packing, algorithms, data compression, source classification, representation theory

Jayce Robert Getz

Assistant Professor in the Department of Mathematics

Keywords in this area
Automorphic representations, arithmetic geometry

Heekyoung Hahn

Assistant Research Professor of Mathematics

Keywords in this area
Littlewood-Richardson semigroup, representations for the classical groups, partitions and q-series

Richard Hain

Professor of Mathematics

Keywords in this area
algebraic geometry

William L. Pardon

Professor of Mathematics

Keywords in this area
Commutative algebra, Quadratic forms

Leslie Saper

Professor of Mathematics

Keywords in this area
intersection cohomology, combinatorics of Weyl groups, K-theory

missing portrait

Chadmark L. Schoen

Professor of Mathematics