Viewing archives for 2006

Akshay Venkatesh

Akshay Venkatesh completed his undergraduate degree at the University of Western Australia, Perth, and received his PhD from Princeton University in 2002 under the direction of Peter Sarnak. His mathematical interests center around number theory and automorphic forms.  He is particularly interested inequidistribution questions on homogeneous spaces, and the interplay between ergodic and spectral techniques.  Akshay was appointed as a Clay Research Fellow for a term of two years beginning 2004.

András Vasy

András Vasy received his PhD from the Massachusetts Institute of Technology in 1997 under the supervision of Richard Melrose. The focus of his research program is partial differential equations in the presence of an additional geometric structure, of a higher rank type.  Examples include scattering theory both for N-body quantum Hamiltonians and on higher rank symmetric spaces, and wave propagation on manifolds with corners.  In 2002 he received the Alfred P. Sloan Research Fellowship.  András was a appointed as a Clay Research Fellow for a term of two years beginning 2004.

David Speyer

David Speyer received his PhD from the University of California, Berkeley in 2005 under the supervision of Bernd Sturmfels.  Much of his research is in the emerging area of tropical geometry, to which he has contributed both fundamental results as well as applications, e.g., a new proof of Horn’s conjecture on eigenvalues of hermitian matrices and (with Lior Pachter) the reconstruction of phylogentic trees from subtree weights. His research interests include continuing work in tropical geometry, cluster algebras and the geometry of grassmannians and flag varieties.  David was appointed as a Clay Research Fellow for a term of five years beginning June 2005.

Samuel Payne

Samuel Payne received his PhD from the University of Michigan in 2006 under the supervision of William Fulton. His thesis,Toric vector bundles, gives a surprising and simple construction of complete toric varieties on which there are no nontrivial equivariant bundles of rank less than or equal to three.  Sam was appointed as a Clay Research Fellow for a term of four years beginning June 2006.

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.

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.

Sergei Gukov

Sergei Gukov received his PhD from Princeton University in 2001 under the supervision of Edward Witten.  Motivated by phenomenological applications, he works on understanding string compactifications on manifolds of reduced holonomy, such as Calabi-Yau four-folds.  Sergei was appointed as a Clay Research Fellow for a term of five years beginning 2001.

Ben Green

Ben Green received his PhD from the University of Cambridge in 2003 under the supervision of Tim Gowers.  Ben was appointed as a Clay Research Fellow for a term of two years beginning July 2005.

The 2004 Clay Research Award was made to Ben for his joint work with Terry Tao on arithmetic progressions of prime numbers.

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.

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