Institute for applied mathematics


Prof. M. Disertori, Dr. Rojas-Molina

 The seminar will take place on  Tuesdays 10-12Room N 0.008




  • October  24         "Introduction to spectral theory for unbounded operators
  • November 7        "Helffer-Sjöstrand representation I"
  • November 14      "Combes-Thomas estimate"
  • November 21      "Helffer-Sjöstrand representation II"
  • December 5        "An application: decay of correlations"
  • December 12      "Another application: homogeneization Part I"
  • December 19      "Another application: homogeneization Part II"








    Description. A large number of problems in mathematical and theoretical physics can be reformulated in terms of a generalized Schrödinger equation of the form

                                                             i∂t ψ = Lψ,

    where L = DRD + V, D is a first oder differential operator, R is a fixed matrix V a multiplication operator. Prominent examples include the standard Schrödinger equation and classical wave equation (like acoustic and Maxwell). A major problem is the study of the corresponding operator kernel δxL-1δy , or more generally of δxf(L)δy where f is a bounded continuous function.

    In this seminar we will learn some fundamental tools to study these problems, namely Combes-Thomas estimate and Helffer-Sjöstrand representation. We will then see two applications.

    (a) Study correlations for gradient type measures of the form

                                                           dμ(φ) = dφΛ e−F(∇φ)

    where φ : Λ → H, with Λ ⊂⊂ Z d , H is a real or complex finite dimensional Hilbert space,  F is C2 and convex, and Λ → Zd

    (b) Prove decay estimates of the form |δxf (L)δy | ≤ g(|x − y|), where g(u)→0 as u→∞.


    Prerequisites. Functional analysis and Introduction to PDE. Some basic knowledge in statistical mechanics may be useful but is not necessary.







    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

    Mailing address

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