This summer school will be mainly devoted to three courses by Ivan Corwin and Martin Hairer on Khardar-Parisi-Zhang (KPZ) equation and Peter Friz on rough paths. Several others talks will present the most recent advances on these topics.
Guiding principle in the courses will be to present the theory of rough paths and recent work by Martin Hairer who managed to solve rigorously the KPZ equation using this theory among other ones. In conjunction with recent breakthroughs on the exact statistics of the KPZ equation (the topic of Ivan Corwin's mini-course), these results will likely validate a number of predictions in the physics literature in which this equation is often seen as a universal limit. The method developed by Martin Hairer will also allow progresses on other very singular equations.