Geometry and Topology
Graduate Courses
The document Graduate Study in Geometry and Topologyoutlines 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
Pierre Albin — Analytic representations of topological invariants, analysis on non-compact or singular spaces, spectral geometry.
Matthew Ando — Homotopy theory, formal groups, analysis on loop spaces, elliptic cohomology and representation theory.
Stephanie Alexander — Differential geometry, global analysis.
Jayadev Athreya — Ergodic theory and dynamics of group actions on parameter spaces of geometric objects.
Yuliy Baryshnikov —Applications of topology in engineering, stochastic geometry and topology.
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.
Rui Loja Fernandes — Differential geometry, Poisson geometry, integrable systems and Lie theory.
George K. Francis — Geometrical graphics, numerical geometry, descriptive topology, differential topology, dynamical systems, low dimensional geometry and 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.
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
Spencer Dowdall — Mapping class groups, low-dimensional topology, Teichmuller theory, geometric group theory.
Martin Frankland — Algebraic topology, homotopy theory.
Jordan Watts — Symplectic geometry and smooth structures.
Faculty Members in Related Areas
John P. D'Angelo — Complex geometry.
Philippe Di Francesco — Mathematical Physics, Enumerative and Algebraic Combinatorics, Integrable models of Statistical Physics, Cluster Algebra, Matrix models, Quantum (Conformal) Field Theory.
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.
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.
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.
Kenneth B. Stolarsky — Number theory, geometry.
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.
Paul E. Schupp — Combinatorial group theory, decision problems, automata theory and formal language theory, computational complexity.