Viewing archives for 2016

Tony Yue Yu

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.

Alex Wright

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

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

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

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

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

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.

James Maynard

James Maynard received his PhD in 2013 from the University of Oxford under the supervision of Roger Heath-Brown and is currently a Fellow by Examination at Magdalen College, Oxford. James is primarily interested in classical number theory, in particular the distribution of prime numbers. His research focuses on using tools from analytic number theory, particularly sieve methods, to study primes. James has been appointed as a Clay Research Fellow for a term of three years beginning 1 July 2015.

June Huh

June Huh received his PhD in 2014 from the University of Michigan under the supervision of Mircea Mustaţă. He applies algebraic geometry and singularity theory to problems in combinatorics and other areas. His recent interests include singularities of projective hypersurfaces, positivity of Chern classes of Schubert varieties, and connections between realizability problems in algebraic geometry and combinatorial geometry. June was appointed as a Clay Research Fellow for a term of five years beginning 1 July 2014.

Simion Filip

Simion Filip will receive his PhD in June 2016 from the University of Chicago under the supervision of Alex Eskin. He is interested in the connections between dynamical systems and algebraic geometry, in particular between Teichmüller dynamics and Hodge theory. His recent interests also involve K3 surfaces and their special geometric properties.  Simion has been appointed as a Clay Research Fellow for a term of five years beginning 1 July 2016.

Photo by Eduard Duryev.

Semyon Dyatlov

Semyon Dyatlov received his Ph.D. from the University of California, Berkeley (May 2013) under the supervision of Maciej Zworski. He applies the methods of microlocal analysis and dynamical systems to problems in scattering theory, quantum chaos, and mathematical general relativity. One of his research interests is scattering resonances, which are complex numbers generalizing the concept of bound states to open systems. Resonances appear in particular when studying long-time behavior of linear waves on noncompact mainfolds, or decay of classical correlations for chaotic flows. In his thesis, Semyon develops a new microlocal framework to describe asymptotics of resonances and phase space concentration of associated resonant states under dynamical assumptions motivated by the wave equations on rotating black holes.

Semyon received his B.Sc. from Novosibirsk State University in 2008. He was a member of MSRI in Fall 2013 and is currently at MIT.  Semyon began his five-year term on 1 July 2013.

Ivan Corwin

Ivan Corwin received his PhD in 2011 from the Courant Institute at New York University under the supervision of Gerard Ben Arous.  His interests include probability, mathematical physics and exactly solvable systems.  One part of his research has been to compute exact formulas for the statistics of the solution to the Kardar-Parisi-Zhang non-linear stochastic PDE.  This stochastic PDE and its statistics describe a large universality class of systems, including growth processes, interacting particle systems, directed polymers in random environments, and less directly random matrix theory.  Ivan was appointed as a Clay Research Fellow for a term of four years beginning July 2012.