Aktuelles

Mittwoch, 15.07.2020: Compact ancient solutions to the Ricci flow in dimension 3

Prof. Dr. Simon Brendle (Columbia University)

Ancient solutions are solutions of geometric flows which are defined infinitely far back in time. Ancient solutions play a key role in the study of the Ricci flow. In particular, Perelman showed that any finite time singularity of the Ricci flow in dimension 3 is modeled on an ancient solution which in addition is k -noncollapsed; these are referred to as ancient k -solutions. In 2018, we obtained a complete classification of all noncompact ancient k -solutions in dimension 3. In these lectures, we will discuss recent work with Panagiota Daskalopoulos and Natasa Sesum which gives a complete classification of all compact ancient k -solutions in dimension 3.

Uhrzeit:	16:15
Ort:	This seminar will meet online. Please sign up by sending an email to Gerhard Huisken.
Gruppe:	Special Lecture Series
Einladender:	G. Huisken

Donnerstag, 16.07.2020: Einbettbarkeit reeller/positiver Matrizen in stark stetige Halbgruppen

A. Radel (FU Berlin)

In diesem Vortrag geht es um die Frage, wann eine (endliche oder unendliche) reelle/positive Matrix T in eine reelle/positive stark stetige Halbgruppe einbettbar ist. Es werden notwendige und hinreichende Kriterien für die Einbettbarkeit gegeben.

Uhrzeit:	13:30
Ort:	Online (Einwahldaten über R. Nagel)
Gruppe:	Oberseminar Funktionalanalysis
Einladender:	R. Nagel

Donnerstag, 16.07.2020: Strong cosmic censorship black hole interior stability analyses on the level of scalar waves

Dr. Anne Franzen (Technical University of Lisbon)

Motivated by the Strong Cosmic Censorship Conjecture, in the presence of a cosmological constant, we consider solutions of the scalar wave equation Box_g\psi=0 on fixed subextremal Reissner--Nordstr\"om--de Sitter backgrounds (\cM, g), without imposing symmetry assumptions on \phi. We provide a necessary condition, in terms of surface gravities and a parameter for an exponential decaying Price law, for a local energy of the waves to remain bounded up to the Cauchy horizon. The energy we consider controls, in particular, regular transverse derivatives at the Cauchy horizon, which allows us to extend the solutions (as functions), to the Cauchy horizon, in C^0\cap H^1_{loc}. This corresponds to another manifestation of the potential breakdown of Strong Cosmic Censorship in the positive cosmological constant setting.

Uhrzeit:	14:15
Ort:	This seminar will meet online. Please sign up by sending an email to Angelika Spörer-Schmidle
Gruppe:	Oberseminar
Einladender:	Cederbaum, Huisken, Kröncke