The 2015 Clay Research Award was made to Larry Guth and Nets Katz for their solution of the Erdős distance problem and for other joint and separate contributions to combinatorial incidence geometry. Their work is an important contribution to the understanding of the interplay between combinatorics and geometry.
The 2015 Clay Research Award was made to Larry Guth and Nets Katz for their solution of the Erdős distance problem and for other joint and separate contributions to combinatorial incidence geometry. Their work is an important contribution to the understanding of the interplay between combinatorics and geometry.
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.
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.
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.
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.
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.