2000. xii+250 pp. Vanishing viscosity solutions of nonlinear hyperbolic systems. Ann. of Math. (2) 161 (2005), no. 1, 223–342 [written with Stefano Bianchini] 2008 Charles Fefferman for "his many fundamental contributions to different areas of analysis" including A sharp form of Whitney's extension theorem. Ann. of Math. (2) 161 (2005), no. 1, 509–577 Whitney's extension problem for . Ann. of Math. (2) 164 (2006), no. 1, 313–359. 2008 Carlos Kenig for "his important contributions to harmonic analysis, partial differential equations, and nonlinear dispersive PDE" including: Well-posedness and scattering results for the generalized Korteweg-de Vries equation via the contraction principle. Comm. Pure Appl. Math. 46 (1993), no. 4, 527–620 [written with Gustavo Ponce and Luis Vega] Global well-posedness of the Benjamin-Ono equation in low-regularity spaces. J. Amer. Math. Soc. 20 (2007), no. 3, 753–798 [written with Alexandru Ionescu] Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Acta Math. 201 (2008), no. 2, 147–212 [written with Frank Merle] 2011 Assaf Naor for "introducing new invariants of metric spaces and for applying his new understanding of the distortion between various metric structures to theoretical computer science" and his "remarkable work [...] on a lower bound in the sparsest cut problem" including On metric Ramsey-type phenomena. Ann. of Math. (2) 162 (2005), no. 2, 643–709 [written with Yair Bartal, Nathan Linial, and Manor Mendel Metric cotype. Ann. of Math. (2) 168 (2008), no. 1, 247–298 [written with Manor Mendel] Euclidean distortion and the sparsest cut. J. Amer. Math. Soc. 21 (2008), no. 1, 1–21 [written with Sanjeev Arora and James R. Lee] Compression bounds for Lipschitz maps from the Heisenberg group to . Acta Math. 207 (2011), no. 2, 291–373 [written with Jeff Cheeger and Bruce Kleiner] 2011 Gunther Uhlmann for "his fundamental work on inverse problems" including The Calderón problem with partial data. Ann. of Math. (2) 165 (2007), no. 2, 567–591 [written with Carlos Kenig and Johannes Sjöstrand] The Calderón problem with partial data in two dimensions. J. Amer. Math. Soc. 23 (2010), no. 3, 655–691 [written with Oleg Imanuvilov and Masahiro Yamamoto] as well as "incisive work on boundary rigidity with L. Pestov and with P. Stepanov and on nonuniqueness (also known as cloaking) with A. Greenleaf, Y. Kurylev, and M. Lassas." 2014 Simon Brendle for "his outstanding solutions of long standing problems in geometric analysis", including Manifolds with 1/4-pinched curvature are space forms. J. Amer. Math.