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Faculty Research Interests
|Last Name||First name||Research Interests||Research Areas|
B.A., Western Washington U.; Ph.D., Princeton, 1974. He 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.
B.A./M.A., University of Missouri/Columbia; Ed.D., University of Missouri/Columbia, 1969. He 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.
B.S., U. of Akron; Ph.D., Ohio State, 1976. Analysis, functional analysis, harmonic analysis. His 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|
Ph.D., Purdue, 2000. Number Theory, Automorphic Forms, and L-functions.
|Automorphic Forms, Number Theory, Representation Theory|
Ph.D., 1987, U. Nac. de Cordoba, Argentina. Representation theory of semisimple Lie groups and analysis on homogeneous spaces.
|Lie Groups, Representation Theory|
B.S./M.S., U.C.L.A.; Ph.D., U.C.L.A., 1982. 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).
I'm interested in the relationship between Dehn surgery and bridge numbers of knots, particularly in the case where the surgery is cosmetic. More generally I enjoy studying Dehn surgery, Heegaard splittings, and knot invariants. I also do some work in topological data analysis.
B.S., University of Detroit; M.S., Purdue University; Ph.D., Wayne State University, 1970. His 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.
Ph.D., Purdue, 2012. Number Theory, Automorphic Forms and Representation Theory.
|Crauder||Bruce||B.A., Haverford College; M.A./Ph.D., Columbia, 1981. Algebraic geometry, mathematics education.|
B.S., OSU; M.A./Ph.D., Michigan, 1971. Low-dimensional topology, mathematics education.
Ph.D., Cornell University, 2004; B.S., University of Illinois (Urbana), 1999. Combinatorial commutative algebra and computational algebra. I am particularly interested in problems involving monomial ideals and their algebraic and combinatorial interpretations.
B.Sc., Imperial College of London; Ph.D., Nottingham, 1981. Analytic number theory, L-functions.
B.A., Fairmont State College; M.A., Penn State; Ph.D., Wisconsin, 1968. Low-dimensional topology, Geometric and Combinatorial Group Theory. His 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.
B.A., Middlebury College; PhD, UC Davis, 2002. The topology of surfaces in 3-dimensional manifolds, such as incompressible surfaces, Heegaard surfaces and bridge surfaces for knots and links.
|Ju||Ning||Ph.D., Indiana, 1999. Applied mathematics.|
B.Sc. (Hon), Australian National University, 1986; M.Sc., Oxford University, 1989; Ph.D., Oklahoma State, 1997. Representation Theory, Number Theory, and Invariant Theory.
|Keener||Marvin||B.S., Birmingham Southern College; M.A./Ph.D., Missouri, 1970. He concentrates on ordinary differential equations.|
Ph.D., Cornell, 2004. Numerical analysis.
|Li||Weiping||B.S., Dalian Institute of Technology; Ph.D., Michigan State, 1992. He 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.|
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.|
|Myers||Robert||B.A./M.A./Ph.D., Rice U., 1977. His 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.|
|Noell||Alan||B.S., Texas A&M; M.A./Ph.D., Princeton, 1983. He 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|
|Pritsker||Igor||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.|
|Ullrich||David||B.A./M.A./Ph.D., Wisconsin, 1981. He 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?|
Ph.D., Texas A&M, 2004. Numerical analysis.
A.B., Cornell U., 1977; Part III, Cambridge U., 1978; A.M./Ph.D., Harvard, 1982. His 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|
B.S., Peking University; Ph.D., University of Chicago, 1996.
Nonlinear partial differential equations from fluid mechanics, geophysics, astrophysics and meteorology. Numerical linear Algebra. He 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|
|Zierau||Roger||B.S., Trinity College; Ph.D., Berkeley, 1985. His areas of research include the representation theory of reductive Lie groups and the geometry of homogeneous spaces.|