2002年 - アメリカ数学会ボッチャー記念賞：波動写像型方程式のソボレフ空間のcritical regularity問題についてのブレイクスルー。(Global regularity of wave maps I. Small critical Sobolev norm in high dimensions, Int. Math. Res. Notices (2001), no.6, 299-328とGlobal regularity of wave maps II. Small energy in two dimensions,Comm. Math. Phys. 224 (2001), no. 2, 443-544.に対して)
Nonlinear dispersive equations. Local and global analysis. CBMS Regional Conference Series in Mathematics, 106. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006. xvi+373 pp. ISBN 0-8218-4143-2
Structure and randomness. Pages from year one of a mathematical blog. American Mathematical Society, Providence, RI, 2008. xii+298 pp. ISBN 978-0-8218-4695-7
Poincaré's legacies, pages from year two of a mathematical blog. Part I. American Mathematical Society, Providence, RI, 2009. x+293 pp. ISBN 978-0-8218-4883-8
Poincaré's legacies, pages from year two of a mathematical blog. Part II. American Mathematical Society, Providence, RI, 2009. x+292 pp. ISBN 978-0-8218-4885-2
An epsilon of room, I: real analysis. Pages from year three of a mathematical blog. Graduate Studies in Mathematics, 117. American Mathematical Society, Providence, RI, 2010. xii+349 pp. ISBN 978-0-8218-5278-1
An epsilon of room, II. Pages from year three of a mathematical blog. American Mathematical Society, Providence, RI, 2010. viii+248 pp. ISBN 978-0-8218-5280-4
(with Van H. Vu) Additive combinatorics. Cambridge Studies in Advanced Mathematics, 105. Cambridge University Press, Cambridge, 2010. xviii+512 pp. ISBN 978-0-521-13656-3
An introduction to measure theory. Graduate Studies in Mathematics, 126. American Mathematical Society, Providence, RI, 2011. xvi+206 pp. ISBN 978-0-8218-6919-2
Topics in random matrix theory. Graduate Studies in Mathematics, 132. American Mathematical Society, Providence, RI, 2012. x+282 pp. ISBN 978-0-8218-7430-1
Higher order Fourier analysis. Graduate Studies in Mathematics, 142. American Mathematical Society, Providence, RI, 2012. x+187 pp. ISBN 978-0-8218-8986-2
Compactness and contradiction. American Mathematical Society, Providence, RI, 2013. xii+256 pp. ISBN 978-0-8218-9492-7
Analysis. I. Third edition. Texts and Readings in Mathematics, 37. Hindustan Book Agency, New Delhi, 2014. xviii+347 pp. ISBN 978-93-80250-64-9
Analysis. II. Third edition. Texts and Readings in Mathematics, 38. Hindustan Book Agency, New Delhi, 2014. xvi+218 pp. ISBN 978-93-80250-65-6
Hilbert's fifth problem and related topics. Graduate Studies in Mathematics, 153. American Mathematical Society, Providence, RI, 2014. xiv+338 pp. ISBN 978-1-4704-1564-8
Expansion in finite simple groups of Lie type. Graduate Studies in Mathematics, 164. American Mathematical Society, Providence, RI, 2015. xiv+303 pp. ISBN 978-1-4704-2196-0
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