Research

Research

Faculty Research Interests

Gene Freudenburg,

Department Chair
My general research area is commutative algebra and affine algebraic geometry. In particular, I study algebraic transformations of polynomial rings and affine spaces, with special attention to certain group actions. My papers include examples of such actions when the ring of invariants is not finitely generated, in both the linear and non-linear cases (Hilbert's 14th Problem). Other papers explore exponential transformations of three-dimensional affine space. The interested reader can find an overview of the subject in my recent book, "Algebraic Theory of Locally Nilpotent Derivations", published by Springer-Verlag.
Christine Browning I am interested in mathematics curriculum development for pre- and inservice elementary/middle school teachers. Within this area of curriculum development, other areas of research interest are on hand-held graphing calculator implementation and assessment of student understanding.
Dwayne Channell My general interests focus on the development of curriculum for the preservice preparation of middle and high school mathematics teachers. More specifically, my interests center on the use of computing technologies in the preparation and professional development of mathematics teachers.
Jon Davis
My research interests include the impact of innovative curricula on students and teachers.  Specifically, I am interested in how teachers use and adapt innovative mathematics curricula during planning and enacting classroom lessons.  In the future, I plan on investigating what and how teachers learn as a result of their use of innovative curricula.
Clifton Ealy My research interests are in finite groups, finite geometries and related graph theory. Recently, I have been studying the genus of finite simple groups, combinatorial structures that arise in the study of finite groups, and quasigroups with identity. I also have interests in some aspects of theoretical computer science, i.e., expander graphs, those related to group theory, and those related to quantum Turing machines.
Paul Eenigenburg I am interested in that part of complex analysis called geometric function theory. Most of the problems involve optimizing a particular functional over special classes of mappings.
Theres Grant My research focuses on understanding the process of teacher change in response to reform efforts in mathematics. In particular I am interested in how elementary teachers’ thinking and practice change in the context of implementing a reform curricula, and what impact adopting innovative mathematics teaching practices has on their teaching of other subject areas (e.g., social studies).
Christian Hirsch My main work focuses on secondary school mathematics curriculum research and development and the impact of innovative curricula on student learning. Currently, I am a Principal Investigator for the NSF-funded Core-Plus Mathematics Project and Co-Director of the NSF-supported Center for the Study of Mathematics Curriculum. Another area of study is the use of innovative curriculum materials as a context for teacher learning.
Terrell Hodge My area of research is the (modular) representation theory and cohomology of algebraic groups and Lie algebras. Much of this work studies and/or is motivated by structures associated to involutions on algebraic groups, such as Lie triple systems.
Ok-Kyeong Kim My research interests are in pre-service and in-service elementary teacher education and children's reasoning in the reformed elementary classrooms.
Kate Kline My research interests involve analyzing how elementary teachers' thinking and practice change in the context of implementing a reform mathematics curriculum, and what hinders and enables this change.
Melinda Koelling I am currently working on computational models of the early stages of visual processing.  I am also interested in generalizations of the Toda lattice.
Yuri Ledyaev Research Interests: control theory, differential equations, nonlinear functional and nonsmooth analysis. More specifically,
  • Optimal control (optimality conditions, problems with state and state/control constraints, nonsmooth optimal control problems, construction of optimal and sub-optimal discontinuous feedback)
  • Differential games (extremal problems in differential games, optimality conditions for strategies)
  • Stabilization of control systems (construction of discontinuous stabilizing feedbacks, robust control, hybrid control)
  • Stability and invariance of solutions of differential equations and inclusions
  • Differential inequalities
  • Nonsmooth analysis (proximal calculus, mean-value principle, applications to control problems) in linear spaces and manifolds
Jane-Jane Lo My area of interest is the development of multiplicative conceptual fields, elementary teacher education and international comparative studies.
Niloufer Mackey My research interests are in matrix analysis and numerical linear algebra, with a focus on the theory and computation of solutions to a variety of structured matrix problems.
John Martino My research field is algebraic topology, and I am particularly interested in the connections between group theory, representation theory, and topology.
Tabitha Mingus My research interests are in the mathematical content preparation of secondary school mathematical teachers and the role of proof as a learning and communication tool in advanced undergraduate mathematics courses.
Annegret Paul My area of research is the representation theory of reductive Lie groups. In particular, I am interested in the unitary dual of reductive groups, and the theta correspondence.
Dennis Pence My recent research interests are collegiate mathematics education with graphing calculators and other technology.
John Petrovic I study the structure theory of bounded linear operators on Hilbert space. I am especially interested in the connection between the operator theory and the theory of functions. While a major part of my research is in pure mathematics, I am always on a lookout for applications - primarily in electrical engineering.
David Richter Mathematical physics, representation theory, algebraic, differential, and classical geometry.
Allen Schwenk My areas of research concentrates on graph theory, especially the eigenvalues of a graph and cospectral graphs. I have also done work on enumeration of various types of trees and graphical enumeration in general. I have an interest in efficient algorithms for searching a family of trees. I also have some interest in combinatorics, especially generating function methods.
Jeff Strom My research specialty is homotopy theory, or, nearly equivalently, algebraic topology. I'm particularly interested in Lusternik-Schnirelmann category, closed classes (and the dual notion, which I call resolving classes), and phantom maps.
Jay Treiman I am currently involved in department adminisitration.
Laura Van Zoest My research involves the preparation of secondary school mathematics teachers. Recent funded projects included four- and five-year-long professional development projects for experienced teachers and a four-year longitudinal study of the development of a group of beginning mathematics teachers. I am particularly interested in the development of mathematics teacher identity in the context of current reforms and the role that communities of learning play in supporting this development.
Arthur T. White I am a topological graph theorist whose primary focus has been the imbeding of Cayley graphs for finite groups onsurfaces.  This can be done to model finite groups, finite fields, and (my most recent interest) finite geometries. Previous interests include self-dual imbeddings, symmetrical maps, generation of block designs, enumerateive topological graph theory, random topological graph theory, and the composition of change-ringing extents.
Ping Zhang My main research interests are in the fields of algebraic combinatorics and graph theory. My recent research involves  coloring, labeling, traversability, distance  and domination in graphs. I am also interested in hyperplane arrangements, combinatorial topology, finite geometry, and number theory.
Qiji Jim Zhu My research interests include techniques of variational analysis and their applications in optimization and control problems.
Steven Ziebarth My research is in assessment and evaluation related to mathematics education. This includes curriculum, student learning and achievement, and teacher training and professional development at the secondary levels.

Revised: March 20, 2007

 

 

 

 


 

 

Department of Mathematics
3319 Everett Hall
Western Michigan University
Kalamazoo MI 49008-5248 USA
(269) 387-4510 | (269) 387-4530 Fax
math-dept@wmich.edu