| 2011 - | Affiliate Professor, Department of Statistics, University of Wisconsin-Madison. |
| 2005 - | Professor, Department of Mathematics, University of Wisconsin-Madison. |
| 2001 - 2005 | Associate Professor, Department of Mathematics, University of Wisconsin-Madison. |
| 1999 - 2001 | Associate Professor, Department of Mathematics, Iowa State University. |
| 1995 - 1999 | Assistant Professor, Department of Mathematics, Iowa State University. |
| 1994 - 1995 | Postdoctoral Fellow, Mittag-Leffler Institute, Sweden. |
| 1993 - 1994 | Postdoctoral Member, Institute for Mathematics and Its Applications, University of Minnesota. |
| 1991 - 1993 | Instructor, Department of Mathematics, The Ohio State University. |
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.
2017 Fellow of the American Mathematical Society, Class of 2018.
2023-2024 Simons Fellow in Mathematics.
Hydrodynamic limits for asymmetric systems. Plenary lecture, NORDSTAT 2002, 19th Nordic Conference on Mathematical Statistics, Stockholm, Sweden, June 9-13, 2002.
Strong law of large numbers for the interface in ballistic deposition. Prize ceremony, 2000 Prix Institut Henri Poincaré-Gauthier Villars, Institut Henri Poincaré, Paris, June 20, 2002.
Limit shapes and fluctuations for some planar stochastic growth models. Plenary lecture, London Mathematical Society Meeting, Bath, September 11, 2006.
Scaling exponents for 1+1-dimensional directed polymers. Plenary lecture, 34th Conference on Stochastic Processes and their Applications SPA 2010, Osaka, Japan, September 6-10, 2010.
KPZ universality for interacting stochastic models. Plenary lecture, Finnish Mathematics Days 2012 (biannual meeting of the Finnish Mathematical Society), Lappeenranta, Finland, January 4-5, 2012.
Directed polymer and percolation models on the plane. IMS Medallion Lecture, Australian Statistical Conference and IMS Annual Meeting, Sydney, July 7-10, 2014.
Variational formulas for directed polymer and percolation models. Invited lecture in the Probability and Statistics Section, International Congress of Mathematicians, Seoul, August 13-21, 2014.
KPZ fluctuation exponents for a class of zero-range processes. Minerva Foundation Lectures, Columbia University, New York, November 2-13, 2015.
The challenges of random growth models. Seymour Sherman Memorial Lecture, Indiana University, Bloomington, April 19, 2019.