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Faculty Research Interests

 

Name Research Interests Research Areas
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 manifestations 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
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.
Mathematics Education
Bruce Crauder B.A., Haverford College; M.A./Ph.D., Columbia, 1981. Algebraic geometry, Mathematics education
Sean Curry Ph.D., University of Auckland, 2016.

Dr. Curry studies conformal, CR (Cauchy-Riemann) and related geometries, in connection with physics and with several complex variables.
Differential Geometry and Geometric Analysis, Several Complex Variables
Allison Dorko B.S. Kinesiology and Physical Education, University of Maine; B.S., Mathematics, Oregon State University; M.S. University of Maine; Ph.D., Oregon State University.

Dr. Dorko is interested in undergraduate mathematics education, specifically student learning from homework and student learning of calculus.
Undergraduate 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 as the structure of the commutator ideals.
Functional Analysis, Operator Theory
John Doyle B.S./M.A./Ph.D. University of Georgia, 2014.

Dr. Doyle's main research interests are in the field of arithmetic dynamics, which is the study of dynamical systems from an algebraic perspective. His research involves techniques from number theory and algebraic geometry, and much of his work deals with moduli spaces which classify dynamical systems with prescribed dynamical behaviors.
Arithmetic dynamics, number theory, arithmetic geometry
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 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
Amit Ghosh B.Sc., Imperial College of London; Ph.D., Nottingham, 1981.

Analytic number theory, L-functions
Neil Hoffman B.A., Williams College; Ph.D., University 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
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
Anthony Kable B.Sc. (Hon), Australian National University, 1986; M.Sc., Oxford University, 1989; Ph.D. Oklahoma State University, 1997. Representation Theory, Number Theory, Invariant Theory
JaEun Ku Ph.D., Cornell, 2004. 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 Melissa is currently a Teaching Assistant Professor at Oklahoma State University and the Director of the Mathematics Learning Success Center. She has done research related to the teaching and learning of mathematical proof, in particular the way that mathematics professors use examples in their proof presentations. She is currently working with a newly established community of mathematics tutoring center directors to collaborate on research related to mathematics learning in tutoring contexts. In particular, she is focusing on tutor-student interactions.  
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.
Geometric Topology
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. Mathematics education
Anand Patel B.S., UC Berkeley, Ph.D., Harvard University, 2013.

Dr. Patel has diverse interests in algebraic geometry. These include:  moduli of curves, classical projective geometry, arithmetic geometry, and enumerative geometry.
Algebraic geometry
Igor Pritsker B.A., M.S., Donetsk State University, USSR, 1990; Ph.D., University of South Florida (Tampa), 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.

Dr. Richmond's mathematical interests include algebraic geometry, algebraic combinatorics, Lie theory and representation theory. He is currently interested in anything related to flag varieties and Schubert varieties.
Algebraic geometry, Algebraic combinatorics, Lie theory, Representation theory
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-Resiner 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 application of mathematical concepts with new technologies, for example 3D printing and virtual/augmented reality.
Three-Dimensional Geometry and Toplogy, 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 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 analysis
Xukai Yan B.S. University of Science and Technology of China; Ph.D. Rutgers University, 2017.

Dr. Yan's research is on analysis of nonlinear partial differential equations and applications, recently working on equations arising from fluid dynamics and mathematical biology.
Partial differential equations, Nonlinear analysis
Xu Zhang B.S./M.S., Sichuan University; Ph.D., Virginia Tech, 2013.

Dr. Zhang's research is on numerical analysis and scientific computing. In particular, he is interested in numerical methods for partial differential equations. Recently, his research focuses on immersed finite element methods for interface problems including algorithm development, implementation, error analysis, and engineering applications.
Numerical Analysis, Scientific Computing
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

Emeritus Faculty

Name 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 quatitative) 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
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 grades 6-12, including AP Calculus.
Complex Analysis
Benny Evans B.S., OSU; M.A./Ph.D., Michigan, 1971. Low-dimensional topology, Mathematics Education
Marvin Keener B.Sc., Birmingham Sourthern College; M.A./Ph.D., Missouri, 1970. Ordinary Differential Equations
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. Four 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

 

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