# Research in algebra

In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. *Source: Wikipedia*

## Professors with interests in algebra

- Bruce Corrigan-Salter
- Daniel Drucker
- Daniel Frohardt
- Daniel Isaksen
- Leonid Makar-Limanov
- Frank Okoh
- Andrew Salch
- Ualbai Umirbaev

## Research areas in algebra

### Group theory

Properties of almost-simple groups, applications to the inverse Galois problem and braid groups.

### Finite groups and finite geometries

Geometries associated with groups of Lie type, generalized n-gons, and their automorphism groups.

### Character theory

Character value estimates infinite groups.

### Non-commutative ring theory

Free algebras, matrix localizations, division rings of quotients of enveloping algebras of Lie algebras, and matrices over these.

### Module theory

Infinite-dimensional modules over finite-dimensional algebras, irreducible modules over Heisenberg algebras.

### Lie algebras, linear algebra, and number theory

Root systems, evaluation of determinants, and Diophantine equations.