Vorträge in der Woche 15.02.2021 bis 21.02.2021

Montag, 15.02.2021: Heat kernals and L2-Betti numbers

Anton Deitmar

Donnerstag, 18.02.2021: Stochastische Reaktion-Diffusionsgleichungen auf Netzwerken

Eszter Sikolya (Budapest)

Auf den Kanten eines endlichen, zusammenhängenden Graphen betrachten wir Reaktion-Diffusionsgleichungen mit stochastischen Störungen (multiplikativen Wienerschen Geräuschen) und Kirchhoffschen Randbedingungen in den Knoten. Nach Konstruktion einer deterministischen Halbgruppe auf allen L^p-Räumen zeigen wir die Existenz und Eindeutigkeit der milden

Donnerstag, 18.02.2021: Enumeration of algebraic and tropical singular hypersurfaces

Uriel Sinichkin ( Tel Aviv University )

It is classically known that there exist (n+1)(d-1)^n singular hypersurfaces of degree d in complex projective n-space passing through a prescribed set of points (of the correct size). In this talk we will deal with the analogous problem over the real numbers and construct, using tropical geometry, Omega(d^n) real singular hypersurfaces through a collection of points in RP^n. We will also consider the enumeration of hypersurfaces with more than one singular point.

Donnerstag, 18.02.2021: Spinors, mass, eigenvalues and rigidity of the Riemannian Schwarzschild manifold

Prof. Dr. Simon Raulot (Université de Rouen)

In this talk, I will present a proof of a generalization of a result of Cederbaum concerning the rigidity of the Riemannian Schwarzschild manifold using spinors. To do so, we will recall a version of the positive mass theorem for asymptotically flat manifolds with compact inner boundary as well as several eigenvalue estimates for the Dirac operator.

Donnerstag, 18.02.2021: The BCS Functional in a Weak Homogeneous Magnetic Field

Marcel Schaub (LMU München)

We provide an asymptotic expansion of the free energy of the BCS model subject to a constant magnetic field. We prove that the instability of the normal state in the superconducting phase is determined by Ginzburg-Landau theory in the weak magnetic field limit. Furthermore, we provide the critical temperature shift caused by the magnetic field. The work is a continuation of a series of papers by Frank, Hainzl, Seiringer, and Solovej. The main difference is the challenging nonperturbative treatment of the magnetic field. We provide considerable simplifications to existing proofs and a new decomposition result for the Cooper pair wave function. Joint work with A. Deuchert and C. Hainzl (to be uploaded soon).