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401-3820-75L 4 Credits DR , MSC D-MATH

Singular Stochastic Partial Differential Equations

Lecturers & Examiners: Dr. Rishabh Sunil Gvalani
Number of participants limited to 15. Fully booked.
VVZ CR n/a

Last Updated: 2026-06-01 11:30:59

Abstract

We will study two approaches to treating singular SPDEs. The first approach is the theory of energy solutions, while the second is the so-called paracontrolled calculus. We will use these two techniques to study two concrete examples: the parabolic Anderson model and the stochastic Burgers equation.

Objective

We will study two approaches to treating singular SPDEs, i.e. SPDEs driven by rough noise which involve operations on distributions (products, composition by regular functions) that do not make classical sense due to the low regularity of the objects involved. The first approach is the theory of energy solutions developed by Gonçalves & Jara and Gubinelli & Jara, while the second is the so-called paracontrolled calculus of Gubinelli, Imkeller, & Perkowski. We will use these techniques to study two concrete examples: the parabolic Anderson model and the stochastic Burgers equation. The course will cover the following topics: I. Energy solutions II. Besov spaces III. Diffusion in a random environment IV. The paracontrolled parabolic Anderson model V. The stochastic Burgers equation

Resources

Lecture Notes

The seminar will follow the following lecture notes by Gubinelli and Perkowski:https://arxiv.org/abs/1502.00157.

General Information

Language
English
Levels
DR , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup End
06.09.2025
Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
seminar Singular Stochastic Partial Differential Equations
in addition some dates Thu 14-16 second half of semester
  • Tue 12:15-14:00 (HG E 22)
  • Thu 14:15-16:00 (CAB G 59)
2 h weekly

Offered In

  • Mathematik Master
    • Seminare und Semesterarbeiten
      • Seminare (ZUR BEACHTUNG: Damit die Zuteilung der verfügbaren Seminarplätze sich nicht primär auf den Zeitpunkt des Einschreibens in die Warteliste stützen muss, haben fast alle Mathematik-Seminare ein spezielles Auswahlverfahren. Eine direkte Belegung in myStudies ist dann nicht möglich, alle kommen zuerst auf die Warteliste. Ausserdem gilt: Die Auswahl an Mathematik-Seminaren wird auf 1 Seminar pro Semester beschränkt. Beachten Sie auch die Lerneinheit 401-0002-99L Generic Seminar - Second Priority / Third Priority.)
  • Doktorat Mathematik (Mehr Informationen unter: )
    • Vertiefung Fachwissen (Die Liste der Lehrveranstaltungen für Doktoratsstudentinnen und Doktoratsstudenten wird jedes Semester im Newsletter der ZGSM veröffentlicht.)