18:00

Doors open.

19:00 – 19:45

Peter Friz (Technical University Berlin, Germany)

Integration - Old and New

The history of integration evolved from Riemann's real analysis in the 19th century to Lebesgue's measure theory. In the 20th century, stochastic integration emerged, with fundamental contributions by Itô. These developments are fundamental in mathematics, probability theory, and modeling randomness in fields like finance and physics. And history goes on: From 1998 onwards, Lyons and later Gubinelli devised rough integration (with first applications to SPDEs around 2010, as will be explained in the talk by Lorenzo Zambotti). The final part of my talk is devoted to a recent unification of rough and stochastic integration theory.

 

20:00 – 20:45

Lorenzo Zambotti (Sorbonne Université, Paris, France)

A Brief History of Stochastic Partial Differential Equations

SPDEs were invented in the early 70s of the 20th century and remained a relatively marginal topic of probability theory, until they were propelled to fame with Martin Hairer’s Fields medal in 2014. In this talk I will try to describe this very active research field, showing some examples of applications and discussing some of the mathematical difficulties in an accessible and informal way. In particular, I will explain how the « rough revolution » which is the topic of Peter Friz’ talk has played a major role in the most recent developments in this area.