Aktuelles

Montag, 03.02.2020: Functional limit theorem for recurrent excited random walks on Markovian cookie stacks

Prof. Dr. Elena Kosygina (Baruch College and the CUNY Graduate Center)

We consider one-dimensional excited random walks (ERWs) on infinitely "high" Markovian cookie stacks which are placed on each site of the one-dimensional integer lattice. We prove a functional limit theorem for these walks in the non-boundary recurrent regime. This work extends some of the previous results about ERWs with "boundedly many cookies per site'' and about ERWs with "periodic cookie stacks''. The limiting process is a Brownian motion perturbed at extrema (BMPE) with explicit parameters. The main challenge in comparison to the previous works and to the transient case is to get a handle on the random environment left by the walk as the walk keeps returning to already visited sites. The main tools are generalized Ray-Knight theorems for local times of ERWs and coupling with a discretized version of BMPE. This is joint work with T. Mountford (EPFL, Switzerland) and J. Peterson (Purdue University, USA).

Uhrzeit:	17:15
Ort:	S7
Gruppe:	Oberseminar Stochastik
Einladender:	Möhle, Teufl, Zerner

Donnerstag, 06.02.2020: On the stability of high-dimensional Kaluza-Klein spaces

Zoe Wyatt (University of Edinburgh)

There are a large class of Kaluza-Klein type spacetimes given by the Cartesian product of 1+n dimensional Minkowski spacetime with a Ricci-flat Riemannian manifold, called the internal space. These are solutions of the vacuum Einstein equations. This talk will show that these spaces are stable as solutions of the Einstein equations when n is sufficiently large and when the internal space has special geometric structure, in particular relating to its holonomy group. The PDE methods required lie at the intersection of methods for quasilinear wave and Klein-Gordon equations. This stability result is related to a conjecture of Penrose concerning the validity of string theory. This talk is based on joint work with Pieter Blue and Lars Andersson.

Uhrzeit:	14:15
Ort:	C9A03
Gruppe:	Oberseminar
Einladender:	Cederbaum / Huisken

Donnerstag, 06.02.2020: Canonical models of toric hypersurfaces

Prof. Dr. Victor Batyrev (Universität Tübingen)

Using combinatorial methods of toric geometry we construct a canonical projective birational model of an arbitrary non-degenerated hypersurface in d-dimensional algebraic torus.

Uhrzeit:	14:15
Ort:	N 15
Gruppe:	Oberseminar Algebraische Geometrie
Einladender:	Batyrev, Hausen, Th. Markwig