The 2007 Clay Research Award was made to Alex Eskin for his work on rational billiards and geometric group theory, in particular, his crucial contribution to joint work with David Fisher and Kevin Whyte in establishing the quasi-isometric rigidity of sol.
The 2007 Clay Research Award was made to Michael Harris and Richard Taylor for their work on local and global Galois representations, partly in collaboration with Laurent Clozel and Nick Shepherd-Barron, culminating in the solution of the Sato-Tate conjecture for elliptic curves with non-integral j-invariants.
The 2007 Clay Research Award was made to Michael Harris and Richard Taylor for their work on local and global Galois representations, partly in collaboration with Laurent Clozel and Nick Shepherd-Barron, culminating in the solution of the Sato-Tate conjecture for elliptic curves with non-integral j-invariants.
The 2007 Clay Research Award was made to Christopher Hacon and James McKernan for their work in advancing our understanding of the birational geometry of algebraic varieties in dimension greater than three, in particular, for their inductive proof of the existence of flips.
The 2007 Clay Research Award was made to Christopher Hacon and James McKernan for their work in advancing our understanding of the birational geometry of algebraic varieties in dimension greater than three, in particular, for their inductive proof of the existence of flips.
Teruyoshi Yoshida received his PhD in 2006 from Harvard University under the supervision of Richard Taylor. His mathematical interest is in the interface between automorphic forms and arithmetic algebraic geometry, with much of his work concerned with the geometric structure of Shimura varieties at places of bad reduction. Teruyoshi was appointed as a Clay Research Fellow for a term of three years beginning December 2007.
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 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 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 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 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 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.