Institute for applied mathematics

 

Prof. M. Disertori, Dr. Rojas-Molina

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

 

 

Program 

  • 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"

 

 

Bibliography

 

     

     

     

    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.

     

     

     

     

     

    News

    Prof. Dr. S. Müller erhält den diesjährigen Lehrpreis der Universität Bonn (07.07.17).

    Prof. Dr. Michael Ortiz kommt als Bonn Research Chair ans IAM (Pressemitteilung, 29.7.2016).

    Prof. Dr. S. Conti erhält den diesjährigen Lehrpreis der Universität Bonn (05.07.2016).

    Prof. Dr. Karl-Theodor Sturm, Koordinator des Hausdorff Zentrums für Mathematik an der Universität Bonn, erhält für seine eigene Forschung einen begehrten Advanced Grant des Europäischen Forschungsrats (ERC). (Pressemitteilung 21.04.2016)

    Contact

    Managing Director: Prof. Dr. Anton Bovier
    Chief Administrator: Dr. B. Doerffel
    geschaeftsfuehrung@iam.uni-bonn.de
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    Mailing address

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