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Pure Mathematics
Analysis
- Dan Coman
- Professor Coman works in the field of several complex variables. His main interests include pluripotential theory and complext dynamics in higher dimensions.
- Tadeusz Iwaniec
- Professor Iwaniec is interested in harmonic analysis and partial differential equations. In particular, he is investigating quasiconformal mappings in n-dimensions and their association with nonlinear equations utilizing variational integrals similar to those arising in nonlinear elasticity.
- Leonid Kovalev
- Professor Kovalev works in geometric mapping theory and related areas of analysis.
- Jani Onninen
- Professor Onninen's area of specialization is Nonlinear Analysis and Geometric Function Theory.
- Evgeny Poletsky
- Professor Poletsky specializes in complex analysis and works mainly with functions of several complex variables. Among his subjects of interest are: invariant metrics, plurisubharmonic functions and holomorphic currents.
- Gregory Verchota
- Professor Verchota studies singular integral operators applied to elliptic boundary value problems for linear equations and systems defined in nonsmooth domains. Recent work has led to new maximum principles for higher order equations.
- Andrew Vogel
- Professor Vogel works in partial differential equations and studies regions on which there are solutions to overdetermined boundary value problems.
Algebra
- Steven Diaz
- Professor Diaz specializes in algebraic geometry (the study of the solutions of polynomial equations in any number of variables) and he focuses largely on curves. His main goal is understanding the moduli spaces which parametrize varying families of curves. Another of his interests is in sets of equations that define finite sets of points.
- Mark Kleiner
- Professor Kleiner works on representations of finite dimensional algebras.
- Graham Leuschke
- Professor Leuschke works in commutative algebra, especially in those aspects closely related to representation theory. He is particularly interested in maximal Cohen-Macaulay modules over Cohen-Macaulay rings.
- Claudia Miller
- Professor Miller works in commutative algebra and its connections with algebraic geometry. Special interests include homological and characteristic p phenomena, as well as intersection theory and multiplicities.
- Declan Quinn
- Professor Quinn is an algebraist who studies group actions on noncommutative rings and Galois theory. His other research interests are Hopf algebras and enveloping algebras.
- Dan Zacharia
- Professor Zacharia studies representations of finite dimensional algebras as well as homological algebra.
Geometry & Topology Research Group
- Douglas Anderson
- Professor Anderson is interested in the interplay between topology and algebraic K-theory. He has used this point of view to investigate questions involving polyhedra, CW complexes, manifolds, transformation groups and pseudoisotopies. He is currently interested in the relationship between controlled topology and lower algebraic K- and L-theories.
- Wu-Teh Hsiang
- Professor Hsiang is applying ideas and techniques from differential equations and Lie group theory to study such differential geometric objects as minimal submanifolds or submanifolds of constant mean curvature.
- Jack Ucci
- Professor Ucci is using the Atiyah-Hirzebruch spectral sequence and the geometry of symmetric products to study the topological K-theory of Eilenberg-MacLane spaces. He is also applying K-theory and equivariant homotopy theory to investigate the suspension order of a finite product of projective spaces.
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