Xinyi Yuan received his PhD from Columbia University in 2008 under the supervision of Shou-Wu Zhang. In his 2006 preprint, “Big Line Bundles over Arithmetic Varieties,” he proves an arithmetic analogue of a theorem of Siu and derives, among other consequences, a natural sufficient condition for when the orbit under the absolute Galois group is equidistributed. Xinyi was apponted as a Clay Research Fellow for a term of three years beginning July 2008.
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.
Sucharit Sarkar received his PhD from Princeton University in 2009 under the guidance of Zoltan Szabo. His research area is in low dimensional topology. His dissertation addressed topics in Heegaard Floer homology for 3-manifolds and knots inside 3-manifolds. Sucharit was appointed as a Clay Research Fellow for a term of five years beginning July 2009.
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.
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.
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.
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.
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 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.