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MSCS > graduate studies > research > Pure Mathematics

Faculty Research - Pure Mathematics

Algebra

A.O.L. Atkin (Emeritus), Ph.D. Cambridge, 1952. Modular forms, number theory.
Paul Fong (Emeritus), Ph.D. Harvard University, 1959. Group theory; representation theory of finite groups.
Daniel Groves, Ph.D. University of Oxford, 2000. Geometric group theory.
Dijana Jakelic, Ph.D. Indiana University, 2000. Representation Theory of Lie Algebras, Quantum Groups, and Hecke Algebras; Combinatorial Representation Theory.
Olga Kashcheyeva, Ph.D. University of Missouri-Columbia, 2003. Algebraic geometry and commutative algebra.
Richard G. Larson (Emeritus), Ph.D. University of Chicago, 1965. Applications of Hopf algebras to control theory and data mining; structure of Hopf algebras and quantum groups; applications of algebra to computer science.
Jeffrey Leon, Ph.D. California Institute of Technology, 1971. Computation group theory; computational combinatorics.
Sharon McCathern, Ph.D. University of Chicago, 2007. Finite p-groups and Lie p-algebras.
Alexey Ovchinnikov, Ph.D. North Carolina State University, 2007. Differential algebra, symbolic computation.
David E. Radford, Ph.D. University of North Carolina, 1970. Hopf algebras; quantum groups; invariants of knots, links and 3-manifolds.
Mark Ronan, Ph.D. University of Oregon, 1978. Groups; geometry.
Stephen Smith (Emeritus), Ph.D. Oxford University, 1973. Finite group theory; combinatorics; computer science; algebraic topology.
Bhama Srinivasan, Ph.D. University of Manchester, 1960. Representation theory of finite groups of Lie type .
Ramin Takloo-Bighash, Ph.D. Johns Hopkins University, 2001. Number Theory.

Number Theory and Algebraic Geometry

Daniel Bernstein, Ph.D. University of California-Berkeley, 1995. Computational number theory; computational commutative algebra; cryptography; computer security.
Alina Cojocaru, Ph.D. Queen's University, 2002. Number Theory, Arithmetic Geometry .
Izzet Coskun, Ph.D. Harvard University, 2004. Algebraic Geometry.
Lawrence Ein, Ph.D. University of California-Berkeley, 1981. Algebraic geometry.
Henri Gillet, Ph.D. Harvard University, 1978. Arithmetic geometry; algebraic geometry; algebraic k-theory.
Olga Kashcheyeva, Ph.D. University of Missouri-Columbia, 2003. Algebraic geometry and commutative algebra.
Anatoly S. Libgober, Ph.D. Tel-Aviv University, 1977. Topology of algebraic varieties; theory of singularities; mirror symmetry.
Mihnea Popa, Ph.D. University of Michigan, 2001. Algebraic Geometry.
Ramin Takloo-Bighash, Ph.D. Johns Hopkins University, 2001. Number Theory.
Jeremy Teitelbaum, Ph.D. Harvard University, 1986. Number theory.
Jan Verschelde, Ph.D. Katholieke Universiteit Leuven, Belgium, 1996. Computational algebraic geometry; symbolic-numeric computation; combinatorial and polyhedral methods; development of mathematical software; high performance computing; numerical analysis.
Philip Wagreich, Ph.D. Columbia University, 1967. Mathematics Education; geometry; integrating mathematics and science; curriculum development.
Stephen Yau, Ph.D. State University of New York-Stonybrook, 1976. Algebraic geometry, singularity theory; complex geometry; CR geometry; nonlinear filtering theory; algebraic geometry code; information theory; control theory; financial math; image database; computer software testing, Bioinformatics.

Analysis

Neil Berger (Emeritus), Ph.D. Courant Institute of Mathematical Sciences, 1968. Elasticity, fluid mechanics.
Calixto Calderon (Emeritus), Ph.D. University of Buenos Aires, 1969. Harmonic analysis; differential equations; mathematical biology and history of science.
Laura DeMarco, Ph.D. Harvard University, 2002. Dynamical systems, complex analysis.
Shmuel Friedland, Ph.D. Technion-Israel Institute of Technology, 1971. Matrices & Applications, Statistical Mechanics, Math. Biology, Dynamical Systems.
Jeff E. Lewis (Emeritus), Ph.D. Rice University, 1966. Analysis: Harmonic Analysis and Partial Differential Equations.
Charles S.C. Lin (Emeritus), Ph.D. University of California-Berkeley, 1967. Operator theory; perturbation theory; functional analysis.
Yoram Sagher (Emeritus), Ph.D. University of Chicago, 1967. Harmonic analysis, interpolation theory, mathematics education.
Roman Shvydkoy, Ph.D. University of Missouri-Columbia, 2001. Fluid mechanics, spectral properties of the linearized Euler equation, stability problems; Stongly continuous operator semigroups, Fourier multipliers, spectral theory; Geometry of Banach spaces.
Zbigniew Slodkowski, Ph.D. Institute of Mathematics of the Polish Academy of Sciences, 1974. Several complex variables.
David Tartakoff (Emeritus), Ph.D. University of California-Berkeley, 1969. Partial differential equations, several complex variables.
Jie Yang, Ph.D. University of Chicago, 2006. Multiple comparisons, Cluster Analysis, Discriminant Analysis, Dimension Reduction, Spatial Statistics, and Financial Mathematics.

Ergodic Theory and Dynamical Systems

Laura DeMarco, Ph.D. Harvard University, 2002. Dynamical systems, complex analysis.
Shmuel Friedland, Ph.D. Technion-Israel Institute of Technology, 1971. Matrices & Applications, Statistical Mechanics, Math. Biology, Dynamical Systems.
Alexander Furman, Ph.D. Hebrew University, 1996. Ergodic theory and Lie groups, especially aspects of rigidity for group actions.
Steven Hurder, Ph.D. University of Illinois-Urbana Champaign, 1980. Differential topology and geometry of foliations; smooth ergodic theory and rigidity of group actions; spectral and index theory of operators.
Howard A. Masur, Ph.D. University of Minnesota, 1974. Dynamical systems; low dimensional topology; Riemann surface theory.

Geometry and Topology

Ian Agol, Ph.D. Univ. of California, San Diego, 1998. Knot theory and 3-manifold topology.
Aldridge K. Bousfield (Emeritus), Ph.D. Massacusetts Institute of Mathematics, 1966. Algebraic topology, homotopy theory.
Marc Culler, Ph.D. University of California-Berkeley, 1978. Group theory; low dimensional topology; 3-manifolds; hyperbolic geometry.
Jason DeBlois, Ph.D. University of Texas - Austin, 2007. Low-dimensional topology, hyperbolic geometry.
Brayton Gray (Emeritus), Ph.D. University of Chicago, 1965. Algebraic topology; homotopy theory.
Daniel Groves, Ph.D. University of Oxford, 2000. Geometric group theory.
James Heitsch (Emeritus), Ph.D. University of Chicago, 1971. Differential topology; theory of foliations; index theory; heat equation methods.
Steven Hurder, Ph.D. University of Illinois-Urbana Champaign, 1980. Differential topology and geometry of foliations; smooth ergodic theory and rigidity of group actions; spectral and index theory of operators.
Louis Kauffman, Ph.D. Princeton University, 1972. Knot theory, topological quantum field theory, quantum topology.
Anatoly S. Libgober, Ph.D. Tel-Aviv University, 1977. Topology of algebraic varieties; theory of singularities; mirror symmetry.
Howard A. Masur, Ph.D. University of Minnesota, 1974. Dynamical systems; low dimensional topology; Riemann surface theory.
Kári Ragnarsson, Ph.D. MIT, 2004. Algebraic Topology.
Peter B. Shalen, Ph.D. Harvard University, 1972. Low-dimensional topology; geometric and combinatorial group theory; hyperbolic geometry.
Brooke Shipley, Ph.D. MIT, 1995. Algebraic Topology and Homotopy Theory.
Martin Tangora (Emeritus), Ph.D. Northwestern University, 1966. Algebraic topology.
Kevin Whyte, Ph.D. Univ. of Chicago, 1998. Geometry of groups and group actions.
John Wood, Ph.D. University of California, Berkeley, 1968. Differential and algebraic topology; topology of nonsingular varieties.

Logic and Universal Algebra

Matthias Aschenbrenner, Ph.D. UIUC, 2001. Logic: Model theory and its applications to algebra and analysis, and constructive methods in algebra.
John Baldwin, Ph.D. Simon Fraser University, 1971. Model theory: stability theory; applications to algebra and universal algebra; finite model theory; random graphs; math education.
Joel Berman, Ph.D. University of Washington, 1970. Universal algebra; ordered sets.
William Howard (Emeritus), Ph.D. University of Chicago, 1956. Proof theory; foundations of mathematics; history of mathematics.
Martin Koerwien, Ph.D. , . Model Theory.
David E. Marker, Ph.D. Yale University, 1983. Mathematical logic; model theory; applications to algebra and geometry, real and complex exponetntation, differential algebra, connections between model theory and descriptive set theory.
Alice Medvedev, Ph.D. University of California - Berkeley, 2007. model theory (a branch of mathematical logic) and algebraic geometry; difference fields.

Combinatorics

Amitava Bhattacharya, Ph.D. Tata Institute of Fundamental Research, 2005. Polyhedral combinatorics, graph theory, convex polytopes (enumerative and algorithmic aspects, optimization), algebraic combinatorics.
Dhruv Mubayi, Ph.D. Univ. of Illinois - C/U, 1998. Combinatorics, especially extremal problems on graphs and hypergraphs.
Uri N. Peled, Ph.D. University of Waterloo, 1976. Graph theory; combinatorial optimization; enumerative combinatorics.
Vera Pless (Emeritus), Ph.D. Northwestern University, 1957. Coding theory; combinatorics.
Vladimir Trifonov, Ph.D. University of Texas at Austin, 2006. Computational complexity, randomized computation, combinatorics.
Gyorgy Turan, Ph.D. Joszef A. University (Hungary), 1981. Complexity theory; computational learning theory; combinatorics; logic.