One of the main concepts underlying modern algebra is the concept of symmetry. Group theory provides methods for studying symmetries of mathematical and physical structures. Lie theory covers the case when a given object has a continuous family of symmetries (think of symmetries of a sphere). The theory of modular forms is devoted to analysis of functions with symmetries. These are some of the areas of expertise of the members of our group. A more detailed list will include: group theory – both algebraic and geometric, semi groups and their applications to automata theory, group algebras, Lie theory, representation theory, modular forms and number theory.
Researcher |
Research Interests |
| Ayse Alaca | Number Theory and Analysis |
| Saban Alaca | Number Theory |
| Yuly Billig | Representation Theory of Infinite-dimensional Lie Algebras, Vertex Algebras, Applications to Soliton Non-linear PDEs |
| Inna Bumagin | Geometric and algorithmic properties of infinite groups, group actions on metric spaces, groups and graphs, Gromov hyperbolic, relatively hyperbolic and automatic groups, efficiency of computations in groups, applications to noncommutative crptography |
| Colin Ingalls | Noncommutative algebra and Algebraic Geometry |
| Paul Mezo | Representations of Algebraic and Metaplectic Groups, Langlands Program, Trace Formula Comparisons, Endoscopy |
| Angelo Mingarelli | Differential Equations, Number Theory, Fuzzy Cellular Automata, Recurrence Relations, Celestial Mechanics |
| Steven Wang | Finite Fields and Applications in Cryptography and Coding Theory, Combinatorics, Algebra and Number Theory |