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

Professor


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

Jo-Ann Cohen

Professor


Topological algebra, ring theory.

Patricia Hersh

Professor


Algebraic and topological combinatorics.

Naihuan Jing

Professor


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

Ricky Liu

Assistant Professor


Algebraic combinatorics, connections to geometry and representation theory.

Kailash Misra

Professor


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

MP

Mohan Putcha

Professor Emeritus


Algebraic monoids, algebraic groups, representation theory.

Nathan Reading

Professor


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

Michael Singer

Professor Emeritus


Ernest Stitzinger

Professor


Lie algebras, group theory, cryptography.

Seth Sullivant

Distinguished Professor, Administrator of Graduate Program


Algebraic statistics, computational and combinatorial algebra, mathematical phylogenetics

Cynthia Vinzant

Assistant Professor


Real algebraic geometry, matrix theory, combinatorics, optimization