2006 Clay Research Fellows Announced
February 2, 2006 (Cambridge, MA) - The Clay Mathematics Institute (CMI) announced today the appointment of Research Fellows Artur Avila, Sophie Morel, and Sam Payne. These outstanding young mathematicians were selected for their research achievements and their potential to make significant future contributions.
Artur Avila (b. 1979), received his Ph.D. in 2001 under the direction of Welington de Melo at the Instituto Nacional de Matemática Pura e Aplicada (IMPA), in Rio de Janeiro, Brazil. His thesis, "Bifurcations of unimodal maps: the topological and metric picture," generalized the regular or stochastic dichotomy from the quadratic family to any non-trivial family of real analytic unimodal maps. Since then he has made numerous outstanding contributions to one-dimensional and holomorphic dynamics, spectral theory of the Schroedinger operator, and ergodic theory of interval exchange transformations and the associated Teichmüller flow. Avila is a chargé de recherche the Centre Nationale de Recherche (CNRS).
Sophie Morel (b. 1979), received her Ph.D. in December 2005 under the direction of Gérard Laumon at the Université de Paris Sud (Orsay). 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.
Sam Payne (b. 1978), will receive his Ph.D. in April, 2006, under the direction of William Fulton at the University of Michigan. His thesis, "Toric bundles," gives a surprising and simple construction of complete toric varieties on which there are no nontrivial equivariant bundles of rank two. In other work, Payne gives counterexamples to conjectures of Fujino and of Hibi (with Mircea Mustata), while his paper "Equivariant Chow cohomology of toric varieties" gives a complete, elegant description of the equivariant Chow cohomology of toric varieties: it is the ring of integral piecewise linear polynomial functions.
Avila, Morel, and Payne join current Clay Research Fellows Daniel Biss, Maria Chudnovsky, Ben Green, Sergei Gukov, Bo'az Klartag, Ciprian Manolescu, Maryam Mirzakhani, David Speyer, András Vasy, and Akshay Venkatesh. For more information, see www.claymath.org/research_fellows.
About the Clay Mathematics Institute
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