## 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.

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.

Jeremiah Heller —Motivic homotopy theory, algebraic cycles and K-theory.

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.

James Pascaleff — Symplectic topology and mirror symmetry.

Charles Rezk — Algebraic topology.

Vesna Stojanoska — Homotopy theory and its relations to arithmetic.

Susan Tolman — Symplectic geometry.

Alexander Tumanov — Complex analysis and geometry.

### Postdoctoral Faculty

Mark Bell — PhD Warwick, 2015. Computational topology, hyperbolic geometry, geometric group theory and dynamical systems.

Dan Berwick-Evans — PhD UC Berkeley, 2013. Quantum field theory and algebraic topology.

Funda Gultepe — PhD Univ of Oklahoma, 2013. Geometric group theory, low dimensional topology, mapping class groups, outer automorphism groups.

Jenya Sapir — PhD Stanford, 2014. Low dimensional topology and geometric group theory.

Ming Xiao — PhD Rutgers, 2015. Several complex variables, Cauchy Riemann geometry, complex geometry.

### 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.

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.

Jing Wang (J.L. Doob Research Assistant Prof) — Fields probability, analysis, and sub-Riemannian geometry. In particular diffusion semigroups on sub-Riemannian manifolds and the related functional inequalities with geometric contents; small time estimations of transition densities of strongly hypoelliptic diffusion processes.

### 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.

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

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.