About Us: Faculty Research Interests

Nir Avni PhD, Hebrew University
Group Theory - Algebraic and arithmetic groups.

Keith Burns PhD, Warwick University (UK)
Keith Burns works on geometrical and dynamical problems connected with geodesics in manifolds with nonpositive curvature. Recent work has concentrated on partial hyperbolicity and stable ergodicity.

Frank Calegari PhD, University of California, Berkeley
Calegari's work in number theory includes the study of Galois representations, in particular their connection to modular forms. He also studies the geometry and analysis of p-adic modular forms. Another interest is the application of arithmetic to questions in geometric topology.

Kevin Costello PhD, University of Cambridge
Kevin Costello works on mathematical aspects of quantum field theory and string theory, as well as on related topics in algebra and geometry.

Leonard Evens PhD, Harvard University (Emeritus)
Evens works on group cohomology and is especially interested in Schur multipliers of p-groups, complexity theory, and computer calculations for group cohomology.

Stephen D. Fisher PhD, University of Wisconson (Emeritus)
Fisher works in complex analysis, recently studying optimal estimation of analytic functions and Mobius invariant spaces of analytic functions.

John Francis PhD, Massachusetts Institute of Technology
Algebraic Topology

John Franks PhD, University of California, Berkeley
Franks's recent topological work has focused on actions of groups on surfaces -- in particular, lattice actions which leave invariant a Borel probability measure on the surface. Some of his earlier work concerned knots that occur as closed orbits of flows, index arguments using the zeta function, subshifts of finite type, attractors, and descriptions of possible dynamics.

George Gasper PhD, Wayne State University (Emeritus)
Gasper's interests include Fourier multipliers, localized potential spaces, and harmonic analysis of special functions, especially the problem of proving the positivity of certain kernels involving special functions. One of his results in the last field played a key role in de Branges's proof of the Bieberbach conjecture.

Ezra Getzler PhD, Harvard University
Getzler has interests ranging over index theory of Dirac operators, Malliavin calculus, cyclic homology, the theory of operads and Gromov-Witten invariants (which lie at the intersection of algebraic geometry, symplectic geometry and theoretical physics).

Paul Goerss PhD, Massachusetts Institute of Technology
Goerss's work is in homotopy theory; in particular. he is interested in combining the algebraic geometry of formal groups and the cohomology of profinite groups to studying stable homotopy theory.

Elton P. Hsu PhD, Stanford University
Hsu's research on stochastic analysis emphasizes applications to parabolic equations in a geometric setting.

Bryna Kra PhD, Stanford University
Kra works in dynamical systems and ergodic theory, with an emphasis on applications to combinatorial number theory.

Mark Mahowald PhD, University of Minnesota (Emeritus)
Mahowald is devising methods to study the stable homotopy groups of spheres while pursuing a variety of problems involving generalized cohomology theories.

Mark Pinsky PhD, Massachusetts Institute of Technology (Emeritus)
Pinsky has worked in probability theory, specifically diffusion processes on manifolds. In recent years he has become interested in classical Fourier analysis, investigating the various implications of the "Pinsky phenomenon".

Stewart Priddy PhD, Massachusetts Institute of Technology (Emeritus)
Priddy's research on the structure of stable homotopy theory uses group theoretic constructions and the tools of group cohomology and modular representation theory.

R.Clark Robinson PhD, University of California, Berkeley
Dynamical Systems: His research in dynamical systems uses analytic and geometric methods. Recent work includes questions relating to attractors, correctly aligned windows to get invariant sets, applications of stable manifold theory to celestial mechanics, and Melnikov method applied to higher dimensional Hamiltonian systems to insure horseshoes.

Michael R. Stein PhD, Columbia University
Stein's current research focuses on certain extensions and generalizations of braid groups. He is also interested in questions concerning central extensions and Schur multipliers of Chevalley groups and Kac-Moody groups over commutative rings.

Andrei Suslin PhD, Leningrad State University
Suslin has made fundamental contribution to algebraic K-theory with special emphasis on higher algebraic K-theory and its connections with and applications to algebraic geometry and algebraic number theory. Suslin is the Board of Trustees Professor of Mathematics.

Dmitry Tamarkin PhD, Penn State University
Algebra and homological algebra; specifically, Tamarkin works on operad theory, non-commutative differential geometry, and the applications of these fields to mathematical physics.

Valentino Tosatti PhD, Harvard University
Differential Geometry and PDE on complex, Kahler and symplectic manifolds, with emphasis on Calabi-Yau manifolds, complex Monge-Ampere equations, Einstein metrics and geometric flows.

Boris Tsygan PhD, Moscow University
Boris Tsygan's interests include non-commutative geometry, index theory, microlocal analysis, deformation quantization, mathematical physics, and sympletic geometry.

Kari Vilonen PhD, Brown University
Kari Vilonen works on representation theory and the geometric Langlands program using methods from topology and algebraic geometry.

Ben Weinkove PhD, Columbia University
My research focuses on partial differential equations and complex geometry. This includes the study of canonical Kahler metrics, the Kahler-Ricci flow and the complex Monge-Ampere equation and its generalizations.

Jared Wunsch PhD, Harvard University
Wunsch studies linear partial differential equations,with emphasis on spectral theory and propagation of singularities for operators on singular spaces.

Zhihong Jeff Xia PhD, Northwestern University
Xia's research is in the areas of Newtonian n-body problem, Hamiltonian dynamics and general hyperbolic and partially hyperbolic dynamical systems.

Sandy Zabell PhD, Harvard University
Professor Zabell's research interests are in the fields of probability and statistics. He is particularly interested in legal applications of statistics, forensic science, and communications security. He is also interested in mathematical logic and the history of mathematics.

Eric Zaslow PhD, Harvard University (Physics)
Mathematical Physics. Zaslow studies mathematical aspects of string theory, most recently focusing on mirror symmetry of Calabi-Yau threefolds. This involves enumerative invariants, minimal submanifolds, and the equivalence of D-brane categories.

Steve Zelditch PhD, University of California, Berkeley
Steve Zelditch works in spectral and scattering theory for Laplacians on Riemannian manifolds, especially the asymptotics of eigenfunctions (quantum chaos) and the inverse spectral problem (Can you hear the shape of a drum). He also works on asymptotics problems on Bergman kernels and metrics that arise in Kaehler geometry, Gaussian random waves and random metrics.

Xinwen Zhu PhD, University of California, Berkeley
I am interested in various aspects of geometrical Langlands program, and in particular its application to number theory.

Seminar Homepages
Dynamical Systems
Geometric Langlands Program