Viewing archives for Research Fellows

Søren Galatius

Søren Galatius received his PhD from Aarhus University in 2004 under the supervision of Ib Madsen. The focus of his research is in algebraic topology, especially the interplay between stable homotopy theory and geometry.  Søren was appointed as a Clay Research Fellow for a term of three years beginning September 2007.

Dennis Gaitsgory

Dennis Gaitsgory received his PhD from Tel Aviv University in 1997 under the supervision of Joseph Bernstein.  His thesis, Automorphic sheaves and Eisenstein series, develops ideas of A. Beilinson, V. Drinfeld and G. Laumon that deal with the geometrization of the theory of automorphic forms. Dennis was appointed as a Clay Research Fellow for a term of four years beginning 2000.

Simion Filip

Simion Filip will receive his PhD in June 2016 from the University of Chicago under the supervision of Alex Eskin. He is interested in the connections between dynamical systems and algebraic geometry, in particular between Teichmüller dynamics and Hodge theory. His recent interests also involve K3 surfaces and their special geometric properties.  Simion has been appointed as a Clay Research Fellow for a term of five years beginning 1 July 2016.

Photo by Eduard Duryev.

Semyon Dyatlov

Semyon Dyatlov received his Ph.D. from the University of California, Berkeley (May 2013) under the supervision of Maciej Zworski. He applies the methods of microlocal analysis and dynamical systems to problems in scattering theory, quantum chaos, and mathematical general relativity. One of his research interests is scattering resonances, which are complex numbers generalizing the concept of bound states to open systems. Resonances appear in particular when studying long-time behavior of linear waves on noncompact mainfolds, or decay of classical correlations for chaotic flows. In his thesis, Semyon develops a new microlocal framework to describe asymptotics of resonances and phase space concentration of associated resonant states under dynamical assumptions motivated by the wave equations on rotating black holes.

Semyon received his B.Sc. from Novosibirsk State University in 2008. He was a member of MSRI in Fall 2013 and is currently at MIT.  Semyon began his five-year term on 1 July 2013.

Maria Chudnovsky

Maria Chudnovsky received her PhD from Princeton University in 2003 under the supervision of Paul Seymour.  Maria made significant contributions to the field of combinatorics and graph theory.  While at Princeton, she solved — in collaboration with P. Seymour, N. Robertson, and R. Thomas — the Strong Perfect Graph Conjecture, one of the best known open problems in combinatorics.  Maria was appointed as a Clay Research Fellow for a term of five years beginning April 2003.

Alexei Borodin

Alexei Borodin received his PhD from the University of Pennsylvania in 2001 under the supervision of Alexandre Kirillov. His research concentrates around asymptotic problems of representation theory of growing families of groups (like symmetric groups or unitary groups), and connections with enumerative combinatorics, random matrix theory, and integrable systems.  Alexei was appointed as a Clay Research Fellow for a term of four years beginning July 2001.

Daniel Biss

Daniel Biss received his PhD from the Massachusetts Institute of Technology in 2002 under the supervision of Mike Hopkins.  Daniel was appointed as a Clay Research Fellow for a term of five years beginning June 2002

Manjul Bhargava

Manjul Bhargava received his PhD from Princeton University in 2001 under the supervision of Andrew Wiles.  His research interests span algebraic number theory, combinatorics, and representation theory.  Bhargava’s research includes fundamental contributions to the representation theory of quadratic forms and to p-adic analysis, as well
as to the representation theory of quadratic forms, to interpolation problems and p-adic analysis, and to the study of ideal class groups of algebraic number fields.  Manjul was appointed as a Clay Research Fellow for a term of five years beginning July 2000.

The 2005 Clay Research Award was made to Manjul for his discovery of new composition laws for quadratic forms and for his work on the average size of ideal class groups.

Roman Bezrukavnikov

Roman Bezrukavnikov received his PhD from Tel Aviv University in 1998 under the supervision of Joseph Bernstein.  Roman was appointed as a Clay Research Fellow for a one-year term beginning August 2001.

Artur Avila

Artur Avila received his PhD from the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in 2001 under the supervision of Welington de Melo.  Since then he has made numerous outstanding contributions to one-dimensional and holomorphic dynamics, spectral theory of the Schroedinger operator, and ergodic theory of interval exchange transformations and the associated Teichmüller flow.  Artur was appointed as a Clay Research Fellow for a term of three years beginning July 2006.

Tim Austin

Tim Austin received his PhD in 2010 from the University of California, Los Angeles, under the supervison of Terence Tao.  His interests cover ergodic theory, metric geometry and geometric group theory.   He has developed new techniques for the analysis of certain nonconventional ergodic averages associated with the phenomenon of multiple recurrence, and has shown how to construct examples of infinite discrete gorups with various novel geometric properties.  Tim was appointed as a Clay Research Fellow for a term of five years beginning July 2010.

Spyros Alexakis

Spyros Alexakis received his PhD from Princeton University in 2005 under the supervision of Charles Fefferman.  In his thesis, he proved a special case of the Desser-Schwimmer conjecture in conformal geometry. More recently he proved the full case. This conjecture characterizes all pointwise Riemannian invariant polynomials in the metric tensor and its derivatives whose integrals over a compact manifold without boundary are invariant under conformal deformations.  Spyros was appointed as a Clay Research Fellow for a term of two years beginning July 2009.