Viewing archives for Research Fellows

Terence Tao

Terence Tao received his PhD from Princeton University in 1996 under the supervision of Elias Stein.  His research is split between real-variable harmonic analysis (especially the study of maximal functions, multilinear operators, and oscillatory integrals), the analysis of non-linear dispersive and wave equations (especially at or near the critical regularity), and the combinatorics arising from the representation theory and symplectic geometry of U(n) (and in particular, the study of honeycombs). Terry was appointed as a Clay Research Fellow for a term of three years beginning in 2001.

The 2003 Clay Research Award was made to Terry for his groundbreaking work in analysis, notably his optimal restriction theorems in Fourier analysis, his work on the wave map equations, his global existence theorems for KdV type equations, as well as for significant work in quite distant areas of mathematics, such as his solution with Allen Knutson of Horn’s conjecture.

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.

Peter Scholze

Peter Scholze obtained his PhD in 2012 under the supervision of Michael Rapoport at the Universität Bonn.  After working about the cohomology of Shimura varieties and the Langlands program, his PhD thesis was about a theory of perfectoid spaces, which gives a method to compare objects in mixed characteristic with objects in equal characteristic  p, with applications to p-adic Hodge theory and the weight-monodromy conjectures.  Peter was appointed as a Clay Research Fellow for a term of five years beginning July 2011.

The 2014 Clay Research Award was made to Peter in recognition of his many and significant contributions to arithmetic algebraic geometry, particularly in the development and applications of the theory of perfectoid spaces. 

Will Sawin

Will Sawin obtained his PhD in 2016 from Princeton University, under the supervision of Nicholas Katz. Since then he has worked with Emmanuel Kowalski as a Junior Fellow at ETH Zürich.

Sawin’s research is wide ranging, but focused on the interactions of analytic number theory and algebraic geometry.  Amongst the many areas in which he has made ground-breaking contributions are the application of étale cohomology to estimates of exponential sums over finite fields and, with Tim Browning, the adaptation of classical counting arguments in analytic number theory to explore compactly supported cohomology in spaces of interest in algebraic geometry.  In a recent paper with Kowalski and Philippe Michel, he used ℓ-adic cohomology to derive new bounds on certain bilinear forms that regularly arise in the study of automorphic forms.  There are important applications, for example in the theory of twisted L-functions.  He has also made many wider contributions to the mathematical community, not least through regular posts on diverse topics on the MathOverflow website.

Will was appointed as a Clay Research Fellow for a term of three years beginning 1 July 2018.

Sucharit Sarkar

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.

Igor Rodnianski

Igor Rodnianski received his PhD from Kansas State University in 1999 under the supervision of Lev Kapitanskii.  His research spans the subjects of partial differential equations, harmonic analysis, and geometry.  Igor was appointed as a Clay Research Fellow for a term of two years beginning July 2002.

Aaron Pixton

Aaron Pixton received his Ph.D. in 2013 from Princeton University under the supervision of Rahul Pandharipande. His research is in enumerative algebraic geometry. The topics he has worked on recently include the tautological ring of the moduli space of curves, moduli spaces of sheaves on 3-folds, and Gromov-Witten theory. Aaron has been appointed as a Clay Research Fellow for a term of five years beginning 1 September 2013.

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.

John Pardon

John Pardon received his PhD in 2015 from Stanford University under the supervision of Yakov Eliashberg. His most recent work concerns the construction of virtual fundamental cycles on moduli spaces of holomorphic curves in symplectic geometry. He is also interested in geometry and low-dimensional topology. John received his AB in Math from Princeton University in 2011. John was appointed as a Clay Research Fellow for a term of five years beginning 1 July 2015.

Mircea Mustaƫă

Mircea Mustaƫă received his PhD from the University of California, Berkeley in 2001 under the supervision of David Eisenbud.  His research interest is in algebraic geometry.  More precisely, he is interested in singularities (connections between jet schemes of algebraic varieties and properties of the singularities, via motivic integration), free resolutions (especially for general sets of points on projective curves and connections with properties of vector bundles on these curves) and toric varieties.  Mircea was appointed as a Clay Research Fellow for a term of three years beginning 2001. 

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.