Institute for applied mathematics

Graduate Seminar (S4B1)

Renormalization Group and nonlinear PDEs

Prof. Dr. M. Disertori, Dr. M. Lohmann





Seminar sessions Tuesdays 8.30–10, room 2.040


In case of question please contact

M. Lohmann lohmann(at) (office 4.036)

M. Disertori  disertori(at) (office 4.045)




Tentative schedule.


  1. (19.04)   Introduction  M. Lohmann
  2. (26.04)   Non-linear heat equation  (Part 1)   L. Lechner
  3. (03.05)   Non-linear heat equation  (Part 2)   L. Borasi
  4. (10.05)   Stochastic versus deterministic, infrared versus ultraviolet                                           N.  Barashkov
  5. (31.05)   Linearized renormalization group     T.  Friesel
  6. (07.06)   Second order perturbation theory     S.  Hilger or M. Lager
  7. (14.06)   Renormalized powers for white noise      J.  Jansen
  8. (21.06)   Fixed point problem     U.  Adil
  9. (31.05)   Completing the proof     M.  Lager or S. Hilger






We consider nonlinear parabolic PDE’s of the form

E :      ∂t u = ∆u + F(u),

where u=u(t,x), t≥0, x∈ Λ ⊂ Rd , the nonlinear function F(u) depends on u  (and possibly some derivatives), and may contain a random part. These equations are ubiquitous on physics. Two examples are the effect of temperature on fluid flows and random deposition in surface growth.

In physics one is often interested in the long time/space behavior of solutions. For that one introduces a mollified version  Eε of the equation, where is a small scale regularization. The large scale behavior should not depend on the choice of the mollifier. From a mathematical point of view (and sometimes also in physics), one wants to understand well-posedness of  i.e., the small time/space behavior of the solution u. The problem is that u is expected to have very weak regularity (it is a distribution) and it is not clear how to set up  the solution theory in distribution space. The strategy is to consider the regularized equation   Eε  and to study the limit ε→ 0. Recently this problem was addressed by Hairer who set up a solution theory for a class of such equations.

In this seminar we plan to consider an alternative approach. This is the so-called rigorous renormalization group analysis, inspired by techniques in theoretical physics. The idea is to reformulate the problem as a fixed point problem in a Banach space. We consider a growing sequence of scales εn= ε 2n and construct a sequence of effective equations  Eεn . We stop as soon as εn =1. The strategy is then to tune the parameters in the starting equation  E=E0 in order for Eεn to have a nice limit as ε→ 0 (equivalent to n → ∞).





To understand the RG strategy we will start by reading part of the paper (dealing with  the problem of long time/space behavior)

-'Renormalization group and asymptotics of solutions of nonlinear parabolic equations' J. Bricmont, A. Kupiainen, G. Lin

Comm. Pure, Appl. Math., 47 (1994), pp. 893–921


We will then proceed with

-'Renormalization Group and Stochastic PDEs', Antti Kupiainen 

Ann. Henri Poincare 17 (2016), 497–535






Prof. Jens Frehse (em.) hat die Golden Commemorative Medal der Fakultät für Mathematik und Physik der Karls-Universität Prag erhalten für sein außerordentliches wissenschaftliches Lebenswerk sowie für seine bedeutenden Beiträge zur Analysis Partieller Differentialgleichungen. (01.06.2018)

Die ehemalige Doktorandin am IAM, Lisa Hartung (aktuell: Courant Institute of Mathematical Sciences, New York), wurde für ihre herausragende Doktorarbeit "Extremal Processes in Branching Brownian Motion and Friends" (Betreuer: Prof. Bovier) mit dem Förderpreis der DMV-Fachgruppe Stochastik ausgezeichnet. Details hier. (14.03.2018)

Prof.  Patrik Ferrari erhält den ersten Alexandros Award zusammen mit Ivan Corwin (Columbia University) und Alexei Borodin (MIT) für den Artikel "Free energy fluctuations for directed polymers in random media in 1+1 dimensions".
Details siehe hier. (12.03.2018)

Frau Dr. Martina Vera Baar erhält den Hausdorff-Gedächtnispreis für die beste Dissertation des akademischen Jahres 2016/17 (Betreuer: Prof. Dr. A. Bovier, IAM). (Pressemitteilung, 24.01.2018)


Managing Director: Prof. Dr. Anton Bovier
Chief Administrator: Dr. B. Doerffel
Imprint | Datenschutzerklärung

Mailing address

Institute for Applied Mathematics
University of Bonn
Endenicher Allee 60
D-53115 Bonn / Germany