Prospective Mathematics Graduate Students: Research

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Keith Burns PhD, Warwick University (England)
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 at 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.

Gui-Qiang Chen PhD, Academia Sinica
Chen's current research on nonlinear partial differential equations focuses on conservation laws, free boundary problems, nonlinear waves, and related problems.

Kevin Costello PhD, University of Cambridge
Costello's interests include algebraic structures related to the moduli spaces of Riemann surfaces, mathematical aspects of string theory, and non-commutative geometry.

Matthew Emerton PhD, Harvard University
Emerton works in number theory and arithmetic geometry. Much of his work has focused on the arithmetic theory of modular forms, using methods both of geometry and of representation theory. He also studies the theory of D-modules on varieties in finite and mixed characteristic.

Stephen Fisher PhD, University of Wisconsin
Fisher works in complex analysis, recently studying optimal estimation of analytic functions and Mobius invariant spaces of analytic functions.

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.

Eric Friedlander PhD, Massachusetts Institute of Technology
Friedlander's recent research has involved algebraic geometry, algebraic K-theory, representation theory of finite dimensional algebras, and algebraic topology. Typically, he seeks relationships and applications across these fields, using techniques from algebraic geometry and homotopy theory.

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 Hsu PhD, Stanford University
Hsu's research on stochastic analysis emphasizes applications to parabolic equations in geometric settings.

Joseph Jerome PhD, Purdue University
His principal interests are in nonlinear and constructive analysis, with applications to transport in semiconductors and ion channels in cell membranes. He has also made detailed studies of convergence of approximations to such models.

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

Chiu-Chu Melissa Liu PhD, Harvard University
Liu works on Gromov-Witten theory, a branch of differential and algebraic geometry inspired by string theory in theoretical physics. She has worked on other problems in geometry and mathematical physics such as integrals on moduli space of curves and on general relativity.

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.

Yuri Manin PhD, Steklov Math. Inst. (Russia)
Manin has done fundamental work in several areas of Mathematics. They can be classified into contributions to algebraic geometry, number theory, differential equations and mathematical physics. Manin is a Board of Trustees Professor of Mathematics.

David Nadler PhD, Princeton University

Mark Pinsky PhD, Massachusetts Institute of Technology 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
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
Robinson's 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 a Board of Trustees Professor of Mathematics.

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

Boris Tsygan PhD, Moscow State University
Boris Tsygan's interests include non-commutative geometry, index theory, and symplectic geometry.

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

Amie Wilkinson PhD, University of California, Berkeley
Wilkinson's research relates to stable ergodicity of systems in Dynamical Systems.

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
Zabell has been active in both probability and statistics, with problems of large deviations and in legal statistics.

Eric Zaslow PhD, Harvard University
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.

Seminar Homepages
Dynamical Systems
Geometric Langlands Program

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