B. Zwicknagl, S. Conti, H. Koch, S. Müller, B. Niethammer, M. Rumpf, C. Thiele, J. López-Velázquez
Thursday, April 10, 2:15 pm, seminar room 0.011 Riccardo Adami (Politecnico di Torino) Miniminzing NLS energy on graphs Owing to the loss of translational symmetry, the Nonlinear Schroedinger Equation on star graphs consisting of at least two infinite edges shows the lack of ground states. In this talk it will be shown how to extend this result to a more general class of graphs with Kirchhoff's (i.e. free) conditions at vertices, and an example will be given in which, on the other hand, the ground state exists. This is a joint work in progress with E. Serra and P. Tilli (Politecnico di Torino).
Thursday, May 8, 2:15 pm, Lipschitz-Saal Paolo Tilli (Politecnico di Torino) A minimization approach to hyperbolic Cauchy problems We will discuss some recent results obtained in collaboration with E. Serra, concerning a minimization approach to a wide family of hyperbolic Cauchy problems. This general and abstract approach, that stems from a conjecture of De Giorgi in a particular case, allows the approximation of solutions to Cauchy problems by functions that minimize suitable functionals in space-time. Also equations with dissipative terms can be treated. Focus will be on recent results and some related open questions.
Thursday, June 26, 2:15 pm, Lipschitz-Saal Peter Gladbach A twice-relaxed sharp-interface limit in multiple slip-plane plasticity. We study a continuum model for plastic slips in multiple parallel slip planes embedded into an elastic crystal. This model contains two length scales, the lattice parameter and the distance of the planes. Generalizing a result by S. Conti, A. Garroni, and S.Mueller, we obtain a sharp-interface limit energy, penalizing edge dislocations. Depending on the scaling law of the two length scales, the limit line-tension energy may feature an iterative relaxation behavior and induce microstructure at multiple length scales. We shall outline the basic steps in proving an upper and a lower bound.
Thursday, July 10, 2:15 pm, seminar room 2.040 Nicholas Alikakos (University of Athens) On the structure of phase transition maps: density estimates and applications The scalar Allen-Cahn ( or Ginzburg- Landau ) equation is related to Minimal Surfaces and Minimal Graphs via the level sets of its solutions. The Vector Allen-Cahn is related to Plateau Complexes. These are non-orientable minimal objects with a hierarchical structure. After explaining these relationships we focus on vector extensions of the Caffarelli-Cordoba Density Estimates (L. Caffarelli and A.Cordoba , Comm. Pure and Applied Mathematics Volume 48, Issue 1, pages 1–12, January 1995). In particular we establish lower co-dimension density estimates. These are useful for studying the hierarchical structure of certain entire vector solutions. We also give applications to minimal solutions (lower bounds, Liouville theorems)
Joint work with: Giorgio Fusco
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)