# Talk by Anno Kurth

Rheinische Friedrich-Wilhelms-Universität Bonn

- begin
- 29 Jun 2018 10:30
- end
- 29 Jun 2018
- venue
- Building 15.22, E1, Room 3013 (INM-6 Library), First floor

**Singular SPDEs, Paracontrolled Calculus and Mild Solutions**

In my talk, I will deal with a technique to solve certain highly singular

stochastic partial di↵erential equations exemplified by the Parabolic Anderson

Model (PAM) formally written as the Cauchy problem.

I will briefly introduce the basic concepts of a solution theory for this kind

of equations called paracontrolled calculus. This theory builds on

Bony’s notion of paraproduct to handle the singular nature of certain SPDEs

by means of a renormalization. The introduced framework stands out to

other solution theories due to on the one hand being powerful enough to

treat a wide class of singular SPDEs and on the other hand being relatively

lightweight as well as connecting stochastics with the modern study of PDEs.

As it turns out, the paracontrolled calculus is based on the notion of weak

solution of PDEs. There are, however, also other concepts generalizing the

classical notion of solution to a PDE. In my master thesis I worked on a

paracontrolled calculus based on such a di↵erent concept called mild solution.

I will introduce the basics of this ’mild paracontrolled calculus’ and

show how to obtain a solution theory analogous to the above.

In order to handle this ’mild paracontrolled calculus’, one has, on a technical

level, to deal with integral operators and needs to understand how to

renormalize them correctly. The basic idea of this procedure will also be

introduced in my talk.

Finally, I will very briefly mention an alternative theory to handle singular

SPDEs.