2008 Archives - Page 3 of 4 - Clay Mathematics Institute

Sophie Morel

Sophie Morel received her PhD from Université Paris-Sud in 2005 under the supervision of Gérard Laumon. Her thesis, Complexes d’intersection des compactifications de Baily-Borel – le cas des groupes unitaires sur Q is an important step forward in the Langlands program. She develops a theory of weight truncation on varieties over finite fields with which she derives a simple description of the intersection complexes on the Baily-Borel compactifications of certain Shimura varieties over finite fields. From this in turn she obtains a formula for the trace of the Frobenius endomorphism on the Euler characteristic of the intersection cohomology. Sophie was appointed as a Clay Research Fellow for a term of five years beginning October 2006.

Maryam Mirzakhani

Maryam Mirzakhani received her PhD from Harvard University in 2004 under the supervision of Curtis T. McMullen. In her thesis she showed how to compute the Weil-Petersson volume of the moduli space of bordered Riemann surfaces. Her research interests include Teichmüller theory, hyperbolic geometry, ergodic theory and symplectic geometry. Maryam was appointed as a Clay Research Fellow for a term of four years beginning July 2004.

The 2014 Clay Research Award was made to Maryam for her many and significant contributions to geometry and ergodic theory, in particular to the proof of an analogue of Ratner’s theorem on unipotent flows for moduli of flat surfaces.

Davesh Maulik

Davesh Maulik received his PhD in 2007 from Princeton University under the supervision of Rahul Pandharipande. His mathematical interests include algebraic geometry and its connections with symplectic geometry, mathematical physics, and combinatorics. His research focus is in the area of Gromov-Witten theory and enumerative geometry. Davesh was appointed as a Clay Research Fellow for a term of five years beginning July 2007.

Ciprian Manolescu

Ciprian Manolescu received his PhD from Harvard University under the supervision of Peter B. Kronheimer. In his thesis he gave a remarkable gluing formula for the Bauer-Furuta invariants of four-manifolds. His research interests span the areas of gauge theory, low-dimensional topology, symplectic geometry, and algebraic topology. Ciprian was appointed as a Clay Reearch Fellow for a term of four years beginning 2004.

Bo’az Klartag

Bo’az Klartag received his PhD from Tel Aviv University in 2004 under the supervision of Vitali Milman. In his thesis Klartag showed that a small number of Minkowski and Steiner symmetrizations suffice to bring a convex body in n-space close to a Euclidean ball. His research interests include geometric problems in high dimension, in particular asymptotic convex geometry. Bo’az was appointed as a Clay Research Fellow for a term of three years beginning September 2005.

Adrian Ioana

Adrian Ioana was born in Romania (1981), he received his B.S. from Unversity of Bucharest and his PhD in 2007 from UCLA under the direction of Professor Sorin Popa. His research interests are von Neumann algebras and orbit equivalence. Adrian, together with Jesse Peterson and Sorin Popa, have proved the existence of a II_1 factor with trivial outer automorphism group. He also showed that any countable group which contains a free subgroup has uncountably many non orbit equivalent actions. Adrian was appointed as a Clay Research Fellow for a term of three years beginning August 2008.

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.

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.

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.

Mohammed Abouzaid

Mohammed Abouzaid received his PhD from the University of Chicago in 2007 under the supervision of Paul Seidel. His thesis used techniques from tropical geometry to give a new approach to the homological mirror symmetry conjecture for toric varieties. He is interested in symplectic topology and its interactions with algebraic geometry and differential topology. Mohammed was apponted as a Clay Research Fellow for a term of five years beginning July 2007.

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