Aktuelles

Donnerstag, 02.11.2017: The Isoperimetric Inequality: Proofs by convex and differential geometry

Penelope Gehring

The Isoperimetric Inequality has many different proofs using methods from diverse mathematical fields. In the talk two methods to prove this inequality will be shown. First the 2-dimensional case will be proven by tools of elementary differential geometry and Fourier analysis. Afterwards the theory of convex geometry will briefly be introduced and will be used to proof the Brunn--Minkowsky-Inequality. Using this inequality, the Isoperimetric Inquality in n dimensions will be shown.

Uhrzeit:	14:15
Ort:	S9
Gruppe:	Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie
Einladender:	Cederbaum, Huisken

Donnerstag, 02.11.2017: The Roesch mass in static, spherical-symmetric spacetimes

Markus Wolff

The main subject of this presentation is a new mass, suggested by Henri Roesch, who used this mass to prove the Null Penrose Conjecture. <br>We will compute this mass on embedded spheres foliating the past pointing light cone of a narrow class of static, spherical-symmetric spacetimes following the computation of the Roesch mass of the Schwarzschild spacetime by Roesch. <br>Therefore we will first construct an extension of the spacetime analogous to the Kruskal extension for Schwarzschild, which requires additional assumptions on the metric of the corresponding spacetimes. The spacetime extension in lightlike coordinates allows an easy description of the past pointing light cone and therefore an easier computation of the Roesch mass. <br>Finally, using the assumed form of the metric, we find fairly easy conditions guaranteeing positivity of the Roesch mass, convergence towards the Bondi mass of the spacetime, and the Null Penrose Conjecture.

Uhrzeit:	15:15
Ort:	S9
Gruppe:	Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie
Einladender:	Cederbaum, Huisken

Donnerstag, 02.11.2017: Interacting dynamics for multi-time wave functions

Lukas Nickel (LMU München)

The natural generalization of the quantum mechanical wave function to the realm of relativity is a multi-time wave function psi(t_1,x_1,...,t_N,x_N), a map on configuration space-time. We describe the challenges to set up evolution equations for such multi-time wave functions. We explain why interaction via potentials, as in the non-relativistic Schrödinger equation, is not possible in the multi-time case. The main part of the talk is about an interacting model by Dirac, Fock, Podolsky from the hour of birth of QED, for which we proved existence and uniqueness of smooth solutions provided a cut-off on the fields is used.

Uhrzeit:	16:15 - 17:15
Ort:	C3N14
Gruppe:	Oberseminar Mathematische Physik
Einladender:	Hainzl, Keppeler, Porta, Teufel, Tumulka