James Carlson
Jim Carlson was President of the Clay Mathematics Institute 2003-2012.
Jim Carlson was President of the Clay Mathematics Institute 2003-2012.
The 2012 Clay Research Award was made to Jeremy Kahn and Vladimir Markovic for their work in hyperbolic geometry: (1) their proof that a closed hyperbolic three-manifold has an essential immersed hyperbolic Riemann surface, i.e. the map on fundamental groups is injective; (2) their solution of the Ehrenpreis conjecture: that given any two compact hyperbolic Riemann surfaces, there are finite covers of the two surfaces which are arbitrarily closed in the Teichmüller metric.
The 2012 Clay Research Award was made to Jeremy Kahn and Vladimir Markovic for their work in hyperbolic geometry: (1) their proof that a closed hyperbolic three-manifold has an essential immersed hyperbolic Riemann surface, i.e. the map on fundamental groups is injective; (2) their solution of the Ehrenpreis conjecture: that given any two compact hyperbolic Riemann surfaces, there are finite covers of the two surfaces which are arbitrarily closed in the Teichmüller metric.
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.
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.
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.
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.
Mohammed Abouzaid received his PhD from the University of Chicago in 2007 under the supervision of Paul Seidel. His thesis used techniques from tropical geometry to give a new approach to the homological mirror symmetry conjecture for toric varieties. He is interested in symplectic topology and its interactions with algebraic geometry and differential topology. Mohammed was apponted as a Clay Research Fellow for a term of five years beginning July 2007.