Summary of Research
The algebra research group focuses on infinite group theory, algebraic geometry, commutative algebra, and combinatorics.
Professor Allen’s research is in group theory and ring theory.
Professor Corson’s research is in geometric ring theory.
Professor Dixon’s research is in infinite group theory. He is mostly interested in structural properties of infinite groups which satisfy some finiteness condition, including locally finite groups, generalized radical groups and locally graded groups. His early research was concerned with the Sylow theory of locally finite groups but more recently he has been concerned with groups satisfying certain rank conditions such as the Prufer rank, the torsion-free rank and finite abelian section rank. He is also interested in groups all of whose subgroups satisfy certain conditions. This includes the study of groups with all subgroups permutable, or subnormal, or f-subnormal. He has also been involved with work generalizing the theorems of Schur, Baer and P. Hall. Infinite dimensional linear groups are also one of his interests.
Find Dr. Dixon’s publications on MathSciNet.
Professor Evans’ research in in infinite group theory.
Dr. Lee’s research lies in the intersection of algebra, combinatorics, geometry, topology, and physics. The algebraic objects he is particularly interested in include cluster algebras, MacDonald polynomials, and Kazhdan-Lusztig polynomials. All of these are motivated by theoretical physics, and have been studied in terms of (co)homologies, algebraic combinatorics, and topological cell decompositions. He uses tools from a wide variety of mathematical areas, including algebraic geometry, commutative algebra, non-commutative algebra, and representation theory.