### Applied Mathematics and Differential Equations

This group within the Department of Mathematics has 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.

### Commutative Algebra and Algebraic Geometry

This group has research interests which include algebraic geometry, algebraic and quantum coding theory, homological algebra, representation theory, and K-theory.

### Discrete Mathematics and Coding 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.

### Groups, Semigroups and Topology

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.

### Mathematical Biology

Faculty in this group 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.

### Mathematics Education

This group has made significant contributions to mathematics education, in areas such as mathematical knowledge for teaching, teacher preparation and development, transforming first and second year undergraduate mathematics experiences, and leading programs for high school and middle school students. Group members have backgrounds in pure and applied mathematics, teacher education, and undergraduate mathematics education research.

### Operator Theory/Operator Algebras

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.