These sessions were recordings as part of the SMRI-MATRIX Online Symposium with Martin Hairer (3–19 February 2021).
Colloquium talk: ‘Taming Infinities’
Abstract: Some physical and mathematical theories have the unfortunate feature that if one takes them at face value, many quantities of interest appear to be infinite! What’s worse, this doesn’t just happen for some exotic theories, but in the standard theories describing some of the most fundamental aspects of nature. Various techniques, usually going under the common name of “renormalisation” have been developed over the years to address this, allowing mathematicians and physicists to tame these infinities. We will dip our toes into some of the conceptual and mathematical aspects of these techniques and we will see how they have recently been used in probability theory to study equations whose meaning was not even clear until recently.
Survey of research directions: ‘Open problems and conjectures in SPDE theory’
Abstract: We will survey a number of open problems and conjectures both within SPDE theory and linking SPDE theory to other areas of mathematics.