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
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 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.
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.