IMPRS Ringvorlesung "Partial Differential Equations"

Date and location: Wednesdays 13:30-15:00 in room G10 (MPI MIS)

• Weyl's isometric embedding theorem
  • Lecturer: Dr. P. Hornung
  • Date: 11, 18, 25. April and 2. May
  • Abstract: We give a (very slightly modified) version of Nirenberg's celebrated proof of the Weyl's problem about the realization of smooth convex metrics on the 2-sphere.

• Discretisation of linear, instationary partial differential equations
  • Lecturer: Prof. W. Hackbusch
  • Date: 9., 16. and 23. May
  • Abstract: The lecture considers the instationary difference equations obtained by discretising partial differential equations. We focus to the three properties: consistency, convergence, and stability. The equivalence theorem states that convergence and stability are (almost) equivalent. Therefore, it is of interest to describe sufficient and/or necessary criteria for stability.

• Variational methods for PDEs: existence of closed geodesics on spheres.
  • Lecturer: Prof. E. Spadaro
  • Date: 30. May and 6., 13. June
  • Abstract:Partial differential equations can be often treated via variational methods. Some of these equations are, indeed, naturally associated to an energy and their solutions correspond to critical points of such an energy. In order to give a glimpse of these techniques, in this lecture we will review the min-max construction of a closed geodesic on a 2-dimensional sphere, as proved by Birkhoff in 1917. In particular, we will discuss the difference between finding minimizers and general stationary points of a functional and, time permitting, will put this result in perspective of recent developments.

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  • Lecturer: Prof. L. Szekelyhidi
  • Date: 27. June and 4., 11., 18. July

Other recommended lectures

at the Max Planck Institute

at the University of Leipzig

• Hauptseminar "Condensed Matter Theory" 
  • Lecturer: Prof. Dr. U. Behn, Prof. Dr. K. Kroy
  • Lectures: Thu. 13:30-15:00, at the ITP (klSr)
  • First lecture: April, 12th

• Evolution equations, theory and applications.
  
  • Lecturer: PD Dr. R. Zacher
  • Lectures: Monday 9-11 (SG 3-10), Thursday 9-11 (Hs 19)
  • Exercise Classes: Thursday 13-15 (SG 3-13)

• Mathematische Statistische Mechanik
  • Lecturer: Prof. Dr. Max v. Renesse
  • Lectures: Mo 11.15 – 12.45 SG 4-11, Di 11.15 – 12.45 HS 14
  • First lecture: April, 10th