Algebra and Combinatorics

Algebra and combinatorics are core areas of mathematics which find broad applications in the sciences and in other mathematical fields. Algebra is the study of algebraic structures, for example, groups, rings, modules, fields, vector spaces, and lattices. Combinatorics is the study of natural structures on discrete (often finite) sets.

Research areas in algebra include the structure and representations of Lie algebras, quantum groups, algebraic groups, toroidal algebras, Leibniz algebras, vertex algebras, and their applications in other areas of mathematics and physics. Research areas in combinatorics include algebraic combinatorics, enumerative combinatorics, geometric combinatorics, topological combinatorics, and their applications. Many faculty in the algebra and combinatorics group do algebra with a combinatorial flavor, or combinatorics with algebraic motivation or using algebraic methods.

Bojko Bakalov


Mathematical physics, Lie algebras, vertex algebras, integrable systems.

Jo-Ann Cohen


Topological algebra, ring theory.

Patricia Hersh

Adjunct Professor

Algebraic and topological combinatorics.

Naihuan Jing


Representation theory, quantum groups, infinite-dimensional Lie algebras and groups, vertex algebras, algebraic combinatorics, quantum computation.

Corey Jones

Assistant Professor

Tensor categories, mathematical physics, operator algebras, higher categories.

Ricky Liu

Associate Professor

Algebraic combinatorics, connections to geometry and representation theory.

Kailash Misra


Representations of Lie algebras, quantum groups, vertex operator algebras; applications in number theory, combinatorics, and statistical mechanics.


Mohan Putcha

Professor Emeritus

Algebraic monoids, algebraic groups, representation theory.

Nathan Reading


Algebraic and geometric combinatorics, especially Coxeter groups, cluster algebras, and lattice-theoretic approaches.

Michael Singer

Professor Emeritus

Ernest Stitzinger


Lie algebras, group theory, cryptography.

Seth Sullivant

Distinguished Professor, Director of Graduate Programs

Algebraic statistics, computational and combinatorial algebra, mathematical phylogenetics

Cynthia Vinzant

Associate Professor

Real algebraic geometry, matrix theory, combinatorics, optimization