2000 Prix Institut Henri Poincaré-Gauthier Villars for an article in the journal Annales de l'Institut Henri Poincaré.
2010 Elected Fellow of the Institute of Mathematical Statistics.
2011 Van Vleck Research Prize, University of Wisconsin-Madison Department of Mathematics.
2014 Institute of Mathematical Statistics Medallion Lecturer.
2014 Invited speaker at the International Congress of Mathematicians in Seoul.
2015 Vilas Faculty Mid-Career Investigator Award, University of Wisconsin-Madison.
2015-2016 Simons Fellow in Mathematics.
2016 Named John and Abigail Van Vleck Chair of Mathematics, University of Wisconsin-Madison.