Georgia Benkart's work involves groups such as the group of invertible complex matrices or the group of matrices whose determinant is 1. Each such group is what is called a Lie group, and it has a Lie algebra associated with it. The Lie algebra for the group of matrices of determinant 1 is just space of all matrices whose trace is 0, together with the product xy-yx.
          Lie algebras have interesting actions on vector spaces and often a beautiful combinatorics connected with them. They arise in many different contexts in physics. For example, the Lie algebra of 3 x 3 matrices of trace 0 acts by multiplication on a 3-dimensional space. Physicists identify the basis elements of that space with 3 quarks. The way quarks behave can be described using some facts about modules for Lie algebras.
          Every Lie algebra has attached to it an infinite-dimensional associative algebra, and the two have the same modules. These associative algebras are examples of noncommutative domains - so they are of interest to ring theorists. Some of my latest work studies associative algebras that are like these algebras - they arose in a very combinatorial way by considering the operators up and down on a set with a partial order. Another part of my current research is devoted to studying the structure of certain (possibly infinite-dimensional) Lie algebras.
          She has recently completed a long-time project which solves a missing piece in the classification of the finite-dimensional simple Lie algebras of prime characteristic.