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.
Tony Yue Yu received his PhD in 2016 from Université Paris Diderot under the supervision of Maxim Kontsevich and Antoine Chambert-Loir. He works on non-archimedean geometry, tropical geometry and mirror symmetry. He aims to build a theory of enumerative geometry in the setting of Berkovich spaces. Such a theory will give us a new understanding of the enumerative geometry of Calabi-Yau manifolds, as well as the structure of their mirrors. It is also intimately related to the theory of cluster algebras and wall-crossing structures. Tony has been appointed as a Clay Research Fellow for a term of five years beginning 1 September 2016.
Photo by Jindie Mi.
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.
Alex Wright received his PhD in 2014 from the University of Chicago under the supervision of Alex Eskin. His recent work concerns dynamics on moduli spaces and special families of algebraic curves that arise in this context. His interests include dynamics, geometry, and especially ergodic theory on homogenous spaces and Teichmüller theory. Alex received his BMath from the University of Waterloo in 2008. He was appointed as a Clay Research Fellow for a term of five years beginning 1 July 2014.
Miguel Walsh was born in Buenos Aires, Argentina. He received his “Licenciatura” degree in 2010 from Universidad de Buenos Aires and his PhD from the same institution in 2012, under the supervision of Román Sasyk. During this period he held a CONICET doctoral fellowship. He is currently based at the University of Oxford. His research so far has focused on inverse problems in arithmetic combinatorics, the limiting behaviour of ergodic averages and the estimation of rational points on curves. Miguel has been appointed as a Clay Research Fellow for a term of four years beginning 1 July 2014.
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 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.
Jack Thorne was born in 1987 in Hereford, England. He received his BA at the University of Cambridge in England. He has since studied at Harvard University and Princeton University under the direction of Richard Taylor and Benedict Gross. He received his PhD in May 2012. His primary research interests are algebraic number theory and representation theory, and the diverse connections between these two subjects. Most recently he has been interested in using automorphy lifting techniques to establish new cases of the Fontaine-Mazur conjecture. Jack was appointed as a Clay Research Fellow for a term of five years beginning July 2012.
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 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 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.