The commutative algebra group has research interests which include algebraic geometry, algebraic and quantum coding theory, homological algebra, representation theory, and K-theory.
Research interests in this group center around structural problems in combinatorics, and coding theory, the study of schemes for encoding data to, for example, efficiently detect errors in transmission.
The interplay between topology, group theory and semigroup theory has yielded a wealth of information in all three mathematical fields. These connections are central to the research of our faculty working in this area.
The Applied Mathematics and Differential Equations group within the Department of Mathematics have a great diversity of research interests, but a tying theme in each respective research program is its connection and relevance to problems or phenomena which occur in the engineering and physical sciences.
Functional integration deals with the mathematical foundations of the Feynman Integral, originally introduced in the 1950s by Richard Feynman. Research with this group involves placing this work on a rigorous foundation.
Operator Theory and Operator Algebras are concerned with the study of linear operators, usually on vector spaces whose elements are functions. The subject is analysis, but because the vector spaces are usually infinite dimensional, the subject has a nice blend of techniques from other areas of mathematics, ranging from algebra to topology to dynamical systems.
Several faculty in the department have a strong interest in problems originating in the life sciences, especially from ecology and neuroscience. The group has significant collaborative relationships with colleagues in the life sciences across campus and at other institutions. Group members have mathematical backgrounds in several areas of pure and applied mathematics, including dynamical systems, partial differential equations, algebraic and differential geometry, topology, control theory, and game theory.
Several of our faculty have made significant contributions to mathematics education, in areas such as teacher preparation, the design of online testing software, and leading programs for high school and middle school students.