Home — 2001

Home — 2001

Home — 2001

Arthur Jaffe was President of the Clay Mathematics Institute 1998-2002.

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The 2001 Clay Research Award was made to Edward Witten for a lifetime of achievement, especially for pointing the way to unify apparently disparate fields of mathematics and to discover their elegant simplicity through links with the physical world.

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The 2001 Clay Research Award was made to Stanislav Smirnov for establishing the existence of the scaling limit of two-dimensional percolation, and for verifying John Cardy’s conjectured relation.

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The 2009 Clay Research Award was made to Ian Agol, Danny Calegari and David Gabai for their solutions of the Marden tameness conjecture, and, by implication through the work of Thurstan and Canary, of the Ahlfors measure conjecture.

The **Langlands program** is a collection of conjectures and theorems that unify the theory of automorphic forms, relating it intimately to the main stream of number theory, with close relations to harmonic analysis on algebraic groups as well as arithmetic algebraic geometry. Since its origins in the winter of 1966-67, when it was laid out in a letter from Langlands to André Weil, it has served as the basis of much deep work, including applications to many famous problems in number theory, e.g., Artin’s conjectures on L-functions, Fermat’s Last Theorem, and the behaviour of Hasse-Weil zeta functions.

The **tameness conjecture** asserts that a hyperbolic 3-manifold with finitely-generated fundamental group is homeomorphic to the interior of a compact 3-manifold (possibly with boundary). The Ahlfors conjecture asserts that the limit set of a finitely generated Kleinian group (i.e. the minimal invariant set on the Riemann sphere, which is the boundary at infinity of hyperbolic 3-space) has either full or zero measure, and in the former case the action of the group on it is ergodic.

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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.

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Mircea Mustaƫă received his PhD from the University of California, Berkeley in 2001 under the supervision of David Eisenbud. His research interest is in algebraic geometry. More precisely, he is interested in singularities (connections between jet schemes of algebraic varieties and properties of the singularities, via motivic integration), free resolutions (especially for general sets of points on projective curves and connections with properties of vector bundles on these curves) and toric varieties. Mircea was appointed as a Clay Research Fellow for a term of three years beginning 2001.

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Sergei Gukov received his PhD from Princeton University in 2001 under the supervision of Edward Witten. Motivated by phenomenological applications, he works on understanding string compactifications on manifolds of reduced holonomy, such as Calabi-Yau four-folds. Sergei was appointed as a Clay Research Fellow for a term of five years beginning 2001.

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Daniel Gottesman received his PhD from the California Institute of Technology in 1997 under the supervision of John Preskill. Daniel started off working on black hole evaporation before becoming interested in quantum computers. His work focuses on quantum error-correcting codes. In particular, he studied a class of codes called stabilizer codes and showed that any stabilizer code could be used to perform fault tolerant quantum computation. Daniel was appointed as a Clay Research Fellow for a term of 20 months beginning January 2001.

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Dennis Gaitsgory received his PhD from Tel Aviv University in 1997 under the supervision of Joseph Bernstein. His thesis, *Automorphic sheaves and Eisenstein series*, develops ideas of A. Beilinson, V. Drinfeld and G. Laumon that deal with the geometrization of the theory of automorphic forms. Dennis was appointed as a Clay Research Fellow for a term of four years beginning 2000.

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Alexei Borodin received his PhD from the University of Pennsylvania in 2001 under the supervision of Alexandre Kirillov. His research concentrates around asymptotic problems of representation theory of growing families of groups (like symmetric groups or unitary groups), and connections with enumerative combinatorics, random matrix theory, and integrable systems. Alexei was appointed as a Clay Research Fellow for a term of four years beginning July 2001.