Aktuelles

Donnerstag, 22.06.2023: A Rigidity Theorem for Asymptotically Flat Static Manifolds and its Applications

Brian Harvie (National Taiwan University)

In general relativity, many physically and mathematically important questions concern the uniqueness of the Schwarzschild space. For example, the black hole uniqueness theorem states that the Schwarzschild space is the only asymptotically flat static manifold with stable minimal boundary, and similar uniqueness questions for photon surfaces and for static metric extensions have recently generated great interest. In this talk, I will present a new approach to these questions that is based on a recently-discovered Minkowski inequality for asymptotically flat static manifolds. We prove that the equality is achieved only on coordinate spheres in the Schwarzschild space under natural boundary assumptions. From this, we derive several new uniqueness theorems for Schwarzschild. Notably, we establish global uniqueness of static metric extensions for the Bartnik data induced by Schwarzschild coordinate spheres in all dimensions less than 8. This is based on joint work Ye-Kai Wang of NYCU.

Uhrzeit:	14:15
Ort:	S9 (C 6 H 05)
Gruppe:	Oberseminar GADR
Einladender:	Cederbaum, Huisken, Metzger

Donnerstag, 22.06.2023: Large deviations in Bose-Einstein condensates

Dr. Simone Rademacher (LMU)

We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose-Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables. We prove that in the limit N to infinity, bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.

Uhrzeit:	16:00
Ort:	C3N14
Gruppe:	Oberseminar Mathematical Physics
Einladender:	Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka

Freitag, 23.06.2023: Analysis on Arithmetic Manifolds

Prof. Dr. Valentin Blomer (Bonn)

Sondervortrag im Rahmen des Erich-Kamke-Kolloquiums. --- Abstract: An arithmetic manifold is a Riemannian manifold with additional arithmetic structure: it is acted on by a commutative algebra of "arithmetically defined'' operators. The most classical example is the complex upper half plane modulo the action of a congruence subgroup of SL(2, Z). The investigation of the analytic properties of the Laplace eigenfunction on such manifolds offers a fascinating interplay of analysis, number theory and automorphic forms.

Uhrzeit:	16:15
Ort:	N3
Gruppe:	Kolloquium
Einladender:	Fachbereich