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Faculty Research Interests


                      Research Interests

   Research Areas

Alan Adolphson

B.A., Western Washington U.; Ph.D., Princeton, 1974. Dr. Adolphson works in number theory and arithmetical algebraic geometry. Particular interests include exponential sums, algebraic varieties over finite fields, cohomology theories, and the algebraic theory of differential equations.

Number Theory,  Arithmetical algebraic  geometry

Douglas B. Aichele

B.A./M.A., University of Missouri/Columbia; Ed.D., University of Missouri/Columbia, 1969. Dr. Aichele is interested generally in issues and trends related to collegiate and school mathematics education. More specifically, curriculum and teacher preparation/professional development, mathematics and science connections, entry-level mathematics curriculum and pedagogy, mathematical structures (geometric and quantitative) for prospective elementary teachers, school geometry curriculum and pedagogy.

Mathematics Education

Dale Alspach

B.S., U. of Akron; Ph.D., Ohio State, 1976. Analysis, functional analysis, harmonic analysis. Dr. Alspach's particular interest is in the geometry of Banach spaces. This involves computations in a variety of function spaces and uses methods from advanced calculus, complex analysis, probability, and other areas.

Geometry of Banach spaces

Mahdi Asgari

Ph.D., Purdue, 2000. Number Theory, Automorphic Forms, and L-functions.

Automorphic Forms, Number Theory, Representation Theory

Leticia Barchini

Ph.D., 1987, U. Nac. de Cordoba, Argentina. Representation theory of semisimple Lie groups and analysis on homogeneous spaces.

Lie Groups, Representation Theory

Birne Binegar

B.S./M.S., U.C.L.A.; Ph.D., U.C.L.A., 1982.  Dr. Binegar is interested in the representation theory of reductive groups and its various manifestions in theoretical physics (via quantization), combinatorics (via Kahzdan-Lusztig theory), algebraic geometry (via associated varities), non-commutative algebra (via universal enveloping algebras), and computational mathematics (via the Atlas for Lie Groups program). 

Representation Theory

James Choike

B.S., University of Detroit; M.S., Purdue University; Ph.D., Wayne State University, 1970.  Dr. Choike's mathematical research interests are topics in complex analysis, especially the behavior of functions near singularities.  His work in mathematics education is focused on issues of effective strategies for teaching students connected with how students learn mathematics, curriculum development in mathematics at grades 6 – 16, issues of instructional design for technology-enhanced distance learning systems, and the design and delivery of professional development materials to mathematics teachers of grades 6 – 12, including AP Calculus.

 Complex analysis

John Cook

Ph.D., University of Oklahoma, 2012.                   Dr. Cook's research program centers on investigating how students think about and learn concepts in abstract algebra. Particularly, he is interested in developing models of student thinking about particular concepts in abstract algebra, and then designing instructional sequences that are compatible with and leverage these ways of thinking. His other research endeavors include the mathematical preparation of pre-service teachers and the efficacy of the co-requisite instruction model.

 Math Education

Bruce Crauder

B.A., Haverford College; M.A./Ph.D., Columbia, 1981. Algebraic geometry, mathematics education.

 Algebraic geometry,  Mathematics  education

Detelin Dosev

M.S., Sofia University "St. Kliment Ohridski"; Ph.D., Texas A&M University, 2009.

Dr. Dosev's research interests lie in the fields of functional analysis and operator theory. He has been working on the classification of the commutators on various Banach spaces as well s the structure of the commutator ideals.

 Functional Analysis,  Operator Theory

Benny Evans

B.S., OSU; M.A./Ph.D., Michigan, 1971. Low-dimensional topology, mathematics education.

 Low-dimensional  topology, Mathematics  education
Paul Fili

A.B., Harvard University; Ph.D., University of Texas at Austin, 2010. Dr. Fili's research interests are in number theory and analysis, primarily focusing on topics relating to the distribution of algebraic numbers and points of small height in arithmetic dynamics. Dr. Fili's work uses techniques from potential theory in both the archimedean and non-archimedean settings in order to prove number theoretic results about heights and dynamical systems.

 Number Theory,  Analysis

Christopher Francisco

Ph.D., Cornell University, 2004; B.S., University of Illinois (Urbana), 1999. Combinatorial commutative algebra and computational algebra. Dr. Francisco is particularly interested in problems involving monomial ideals and their algebraic and combinatorial interpretations.

Commutative algebra

Anne-Katrin Gallagher

M.S./Ph.D., The Ohio State University, 2004. Habilitation, University of Vienna, 2014. Dr. Gallagher is interested in: How to use L^2-methods in the construction of holomorphic functions, and how convexity-like conditions imposed on a domain influence the behavior of its holomorphic functions.

 Several Complex    Variables

Amit Ghosh

B.Sc., Imperial College of London; Ph.D., Nottingham, 1981. Analytic number theory, L-functions.

 Analytic number theory, L-functions
Neil Hoffman

BA Williams College; Ph.D. Univeristy of Texas, 2011. Low-dimensional topology, knot theory, hyperbolic 3-manifolds. Dr. Hoffman focuses on problems in low-dimensional topology relating to knot theory, triangulations, commensurability, and the algorithmic classification of 3-manifolds.

Low dimensional topology, knot theory, triangulations, hyperbolic geometry
Weiwei Hu

B.A., Chengdu University of Technology; M.E., Beijing Institute of Information and Control; M.S./Ph.D., Virginia Tech, 2012. Dr. Hu's research focuses on the development of theoretical and computational approaches to optimal design and control of infinite dimensional systems governed by partial differential equations. My current research includes:

Approximation and mathematical control theory of partial differential equations; Well-posedness and long-time behavior of mathematical fluid dynamics; Control and optimization of network dynamics; Computational methods for optimal control design and model reduction.

 Partial Differential  Equations

William Jaco

B.A., Fairmont State College; M.A., Penn State; Ph.D., Wisconsin, 1968. Low-dimensional topology, Geometric and Combinatorial Group Theory. Dr. Jaco's primary interest is in the study, understanding, and classification of three-manifolds. The mathematical questions and techniques in low-dimensional topology are very similar to those in geometric and combinatorial group theory. Much of this work involves decision problems, algorithms, and computational complexity. Recent work has been the connection of combinatorial structures to the geometry and topology of three-manifolds.

Low-dimensional Topology/Geometry

Ning Ju

Ph.D., Indiana, 1999. Applied mathematics.

 Applied Mathematics

Anthony Kable

B.Sc. (Hon), Australian National University, 1986; M.Sc., Oxford University, 1989; Ph.D., Oklahoma State, 1997. Representation Theory, Number Theory, and Invariant Theory.

 Representation Theory, Number Theory, Invariant Theory

Marvin Keener

B.Sc. (Hon), Australian National University, 1986; M.Sc., Oxford University, 1989; Ph.D., Oklahoma State, 1997. Representation Theory, Number Theory, and Invariant Theory.

 Representation  Theory, Number  Theory, Invariant  Theory 

JaEun Ku

Ph.D., Cornell, 2004. Numerical analysis.

Numerical Analysis

Jiri Lebl

B.A./M.A., San Diego State University; Ph.D., University of California, San Diego, 2007.

Dr. Lebl is interested in Several Complex Variables, particularly CR geometry.

 Several Complex  Variables, Analysis

Weiping Li

B.S., Dalian Institute of Technology; Ph.D., Michigan State, 1992. Dr. Li is interested in Floer homologies of instantons on 3-manifolds and Lagrangian intersections; semi-infinite homology of infinite Lie algebras; mapping class groups and knot theory.

Lisa Mantini

B.S., University of Pittsburgh, A.M./Ph.D. Harvard University, 1983. Dr. Mantini's research interests include groups, their actions as symmetries (of a shape in space, of the state space for a vibrating molecule or for the solutions to Maxwell's equations), and the matrix representations of these actions.  Lately she has become an origami enthusiast and is studying symmetric colorations of regular polyhedra and the corresponding representations of their symmetry groups.  Dr. Mantini's interests in mathematics education include the teaching and learning of collegiate mathematics, from studying what professors actually do in the college math classroom, to how we assess student work, to how students learn to read and write proofs. Lately her work has focused on the role of collaborative learning in the teaching of calculus.

Group theory and symmetry, Mathematics education

Jeff Mermin B.S., Duke University, 2000; Ph.D., Cornell University, 2006. Dr. Mermin is particularly interested in questions involving monomial ideals and their algebraic and combinatorial properties. Combinatorial commutative algebra

Melissa Mills

Dr. Mill's research interests are the teaching and learning of mathematical proof. Her dissertation research is an exploratory study investigating the teaching of proof courses at the undergraduate level, particularly the ways that instructors use examples when presenting proof, and how they interact with students in the classroom.

Robert Myers

B.A./M.A./Ph.D., Rice U., 1977. Dr. Myers' research area, geometric topology, is the study of spaces called manifolds. These are generalizations of the curves and surfaces encountered in calculus. The subject has close ties to group theory and geometry. One particularly rich source of examples and applications, which is also very accessible and easy to visualize, is knot theory. This is exactly what its name implies: the mathematical study of knotted curves in ordinary space.

Alan Noell

B.S., Texas A&M; M.A./Ph.D., Princeton, 1983. Dr. Noell is interested in complex analysis in one and several variables. His main area of work involves convexity properties of certain subsets of complex Euclidean space.

Complex analysis

Michael Oehrtman

B.S., Oklahoma State University; Ph.D., University of Texas at Austin, 2002.

Igor Pristsker

B.A., M.S. Donetsk State University, USSR, 1990, Ph.D. University of South Florida, Tampa, FL, 1995. Complex Analysis, Approximation Theory, Potential Theory, Analytic Number Theory and Numerical Analysis.

 Complex Analysis
Ed Richmond

B.A., Colgate University; Ph.D., University of North Carolina, 2008.

Walter Rusin

B.A., Warsaw School of Economics; B.Sc., Warsaw University; M.Sc./Ph.D., University of Minnesota, 2010.

Jay Schweig

B.S., George Mason University; M.S./Ph.D., Cornell University, 2008. Dr. Schweig's research mostly centers around using combinatorial methods to solve problems in algebra. This has included using classical graph and hypergraph invariants to study Stanley-Reisner ideals, and using algebraic invariants and concepts to better understand the structures of objects like matroids and shellable simplicial complexes.

 Algebraic    combinatorics,  Commutative algebra

Henry Segerman

MMath., University of Oxford; Ph.D., Stanford University, 2007. In geometry and topology, Dr. Segerman is mainly interested in triangulations of three-manifolds: their uses in the geometry and invariants of three-manifolds, computation using triangulations, and the structure of the set of triangulations of a three-manifold under local moves. He is also interested in the visualization and applicaiton of mathematical concepts with new technologies, for example 3D printing and virtual/augmented reality.

Three-Dimensional Geometry and Topology, Mathematical Visualization

Michael Tallman

B.S./M.A., University of Northern Colorado; Ph.D., Arizona State University, 2015.  Dr. Tallman's primary research focus is in the area of mathematical knowledge for teaching secondary and post-secondary mathematics. His work informs the design of teacher preparation programs and professional development initiatives through an investigation of the factors that affect the nature and quality of the mathematical knowledge teachers leverage in the context of teaching. In particular, his research examines how various factors like curricula, emotional regulation, identity, and teachers' construction and appraisal of instructional constraints mediate the enactment  of their mathematical and pedagogical knowledge. 

 Mathematical  Education

David Ullrich

B.A./M.A./Ph.D., Wisconsin, 1981. Dr. Ullrich works with Fourier series, complex/harmonic analysis, and various connections with probability theory. For example: What happens if you choose the coefficients in a Fourier series at random? Or, what does Brownian motion have to do with analytic functions?

 Fourier series,  Complex/harmonic  analysis

Yanqiu Wang

Ph.D., Texas A&M, 2004. Numerical analysis.

Numerical Analysis

David Wright

A.B., Cornell U., 1977; Part III, Cambridge U., 1978; A.M./Ph.D., Harvard, 1982. Dr. Wright's primary interest is the study of the properties of algebraic number fields, in particular, those properties (discriminants, class-numbers, regulators) that can be studied with tools from the theory of algebraic matrix groups. This theory dates back to the work of Gauss on the theory of equivalence of binary integral quadratic forms. He also studies the theory of Riemann surfaces and Kleinian groups, a subfield of complex analysis. Surprisingly, many concepts in algebraic number theory have very precise analogues in the theory of surfaces. He is particularly interested in the properties of limit sets of Kleinian groups and in the shape of Teichmuller space, which is a kind of parameter space for Riemann surfaces. See Indra's Pearls, (Mumford, Series, Wright).

Number Theory, Kleinian Groups

Jiahong Wu

B.S., Peking University; Ph.D., University of Chicago, 1996. Nonlinear partial differential equations from fluid mechanics, geophysics, astrophysics and meteorology. Numerical linear Algebra.  Dr. Wu is interested in the analysis, computations and applications of these partial differential equations. One issue he has been working on is whether or not these partial differential equations are globally well-posed.

Nonlinear partial differential equations, mathematical fluid mechanics, numerical computation and analysis

Roger Zierau

B.S., Trinity College; Ph.D., Berkeley, 1985. Dr. Zierau's areas of research include the representation theory of reductive Lie groups and the geometry of homogeneous spaces.

 Representation  Theory