University of Illinois at Urbana-ChampaignDepartment of Mathematics
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Geometry and Topology

Graduate Courses
The document Graduate Study in Geometry and Topology outlines the general areas of geometry and topology studied here and describes the advanced undergraduate and graduate courses that are offered regularly.

Faculty Members in Geometry and Topology
Matthew Ando Homotopy theory, formal groups, analysis on loop spaces, elliptic cohomology and representation theory.
Stephanie Alexander Differential geometry, global analysis.
Maarten Bergvelt Completely integrable systems, Infinite dimensional Grassmannians, vector bundles and gauge theory.
Steven Bradlow Differential geometry, gauge theory, holomorphic vector bundles, moduli spaces.
Nathan Dunfield 3-dimensional geometry and topology, hyperbolic geometry, geometric group theory, experimental mathematics, connections to number theory.
George K. Francis Geometrical graphics, numerical geometry, descriptive topology, differential topology, dynamical systems, low dimensional geometry and topology.
Robert Ghrist Topology (contact geometry/topology, Morse theory, braid theory), dynamics (flows, bifurcation theory, Conley index), and applications (fluids, robotics, computational topology).
Ely Kerman Hamiltonian dynamics and symplectic topology
Christopher Leininger Mapping class groups, Teichmüller theory, knot theory and three-manifolds, and hyperbolic geometry.
Eugene Lerman Symplectic geometry, symmetric Hamiltonian systems.
Anton Malkin Geometry and representation theory
Randy McCarthy Spectra, Calculus of Functors, K-theory.
Igor Mineyev Geometric group theory, large-scale geometry, hyperbolic groups, various types of homology and cohomology of groups and spaces, topology of manifolds and cell complexes, metric conformal structures, metric geometry.
Charles Rezk Algebraic topology.
Susan Tolman Symplectic geometry.
Alexander Tumanov

Complex analysis and geometry.

Postdocs in Related Areas
Bertrand Guillou Homotopy theory, motivic cohomology, algebraic K-theory
Jiri Lebl Several complex variables, real and complex geometry

John Mackay

Metric geometry, analysis on metric spaces, geometric group theory, hyperbolic groups.
Faculty Members in Related Areas
John P. D'Angelo Complex geometry.
Zoltan Furedi Theory of finite sets with applications in geometry, designs, and computer science.
Aimo Hinkkanen Complex analysis, geometry, dynamics.
Sergei Ivanov Combinatorial group theory and its applications.
Ilya Kapovich Geometric and combinatorial group theory.
Sergiy Merenkov Geometric theory of conformal and quasiconformal maps, with applications to areas such as geometric group theory and analysis on fractals.
Igor Nikolaev Investigations of spaces of bounded curvature. Regularity of the generalized solutions of the Monge-Ampere equation
Julian I. Palmore Dynamical systems, celestial mechanics.
Zhong-Jin Ruan Operator algebra.
Paul E. Schupp Combinatorial group theory, decision problems, automata theory and formal language theory, computational complexity.
Kenneth B. Stolarsky Number theory, geometry.
Jeremy Tyson Geometric function theory, quasiconformal maps, analysis in nonsmooth metric spaces, sub-Riemannian geometry.
Adjunct Faculty
Hillel Gauchmann

James F. Glazebrook Differential Geometry and its Applications to Mathematical Physics; Index Theory and Foliations; Holomorphic Vector Bundles; Noncommutative Geometry
Emeriti Faculty
John Ralph Alexander, Jr. Combinatorial geometry, integral geometry.
Ararat Babakhanian Algebraic geometry, homological algebra, ordinary differential equations.
I. David Berg Operator theory, spectral theory, almost periodic functions, manifolds with boundary, spaces of bounded curvature.
Richard L. Bishop Differential geometry, control theory, dynamical systems, Lie groups.
Robert F. Craggs Geometric topology and combinatorial group theory.
John W. Gray Category theory and topology with applications in theoretical computer science and higher dimensional category theory.
Wolfgang R. G. Haken Low dimensional topology, algorithms.
Mary-Elizabeth Hamstrom Low dimensional topology, geometric topology, PL-topology, point set topology.
Richard P. Jerrard Geometric topology, PL-topology, general topology.
Franz W. Kamber Foliation theory, differential geometry, global analysis, characteristic classes, gauge theory.
Howard O. Osborn Differentiable manifolds and fiber spaces.
R. Ranga Rao Reductive groups and their representations , harmonic analysis on homogeneous spaces.
Philippe Tondeur Differential geometry, foliation theory, gauge theory, moduli spaces, low dimensional geometry and topology, topological quantum field theory.
John E. Wetzel Classical and combinatorial geometry.
Emeriti Faculty in Related Areas
Robert Carroll

Transmutation of operators, scattering theory, special functions and integral transformations, inverse problems, symmetric spaces and Lie theory, soliton mathematics.

Daniel R. Grayson Algebraic geometry, K-theory.
Horacio Porta Analysis, differential geometry.

 

Department of Mathematics
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1409 W. Green Street, Urbana, IL 61801 USA
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