the Yang-Mills flow in higher dimensions Alex Eskin, Billiards and lattices Juha Heinonen, On the existence of quasiregular mappings2003 at Duke Bennett Chow, Harnack estimates of Li–Yau–Hamilton type for the Ricci flow Anda Degeratu, Geometrical McKay Correspondence Ron Donagi, Griffiths' intermediate Jacobians, integrable systems, and string theory John Etnyre, Legendrian knots in high dimensions Joe Harris, Are Cubics Rational? Claude LeBrun, Zoll Manifolds, Complex Surfaces, and Holomorphic Disks John Morgan, Variations of Hodge structure for 1-parameter families of Calabi–Yau three-folds Madhav Nori, A modified Hodge conjecture Justin Sawon, Twisted Fourier–Mukai transforms for holomorphic symplectic manifolds Wilfried Schmid, Automorphic distributions, L-functions, and functional equations Jeff Viaclovsky, Fully nonlinear equations and conformal geometry Claire Voisin, K-correspondences and intrinsic pseudovolume forms2004 at Courant Jean-Michel Bismut, The Hypoelliptic Laplacian on the Cotangent Bundle Yasha Eliashberg, Positive Loops of Contact Transformations Blaine Lawson, Projective Hulls and the Projective Gelfand Transformation Dusa McDuff, Applications of J-holomorphic Curves Xiaochun Rong, Local splitting structures on nonpositively curved manifolds Dennis Sullivan, Algebraic topology in string backgrounds Gang Tian, Extremal Metrics and Holomorphic Discs Edward Witten, Gauge Theory Scattering From Curves In CP32005 at Stony Brook Nancy Hingston, Periodic solutions of Hamilton's equations on tori Sergiu Klainerman, Null hypersurfaces and curvature estimates in general relativity Bruce Kleiner, Singular structure of mean curvature flow Frank Pacard, Blowing up Kähler manifolds with constant scalar curvature Rahul Pandharipande, A topological view of Gromov-Witten theory Igor Rodniansky, Non-linear waves and Einstein geometry Yum-Tong Siu, Methods of singular metrics in algebraic geometry Katrin Wehrheim, Floer theories in symplectic topology and gauge theory2006 at Penn Jeff Cheeger, Differentiation, bi-Lipschitz nonembedding and embedding Charles Fefferman, Fitting a smooth function to data Helmut Hofer, On the analytic and geometric foundations of symplectic field theory Ko Honda, Reeb vector fields and open book decompositions William H. Meeks, The Dynamics Theorem for embedded minimal surfaces Yair Minsky, Asymptotic geometry of the mapping class group Frank Morgan, Manifolds with Density Zoltan Szabo, Link Floer homology and the Thurston norm2007 at Maryland Dan Freed, Secondary differential-geometric invariants, generalized cohomology, and QCD Xiaobo Lu, Mean curvature flow for isoparametric submanifolds Vitali Kapovitch, Some open problems in comparison geometry Maryam Mirzakhani, Lattice point asymptotics and conformal densities on Teichmüller space Charles Epstein, Stein fillings and index theorems Guoliang Yu, Group actions and K-theory Simon Brendle, Blow-up phenomena for the Yamabe PDE in high dimensions2008 at Duke Michael Anderson, Conformally compact Einstein metrics with prescribed