Oberseminar Analysis in Geometrie und Physik

C. Bär, M. Keller, M. Klein, J. Metzger, S. Paycha, S. Roelly

Sommersemester 2016

Es werden Themen aus dem Grenzbereich zwischen Differentialgeometrie, mathematischer Physik und stochastischer Analysis behandelt.

Seminarthema:

Einführung in metrische Maßräume

Wann:

Montags, 16.15-17.45

Wo:

Campus Golm, Haus 9, Raum 0.14

Seminarplan (Vorträge):

Datum Vortrag Referent Inhalt
18.04.16Convergence of measuresMoritz Gerlach[Shioya, chapter 1.2 up to Thm 1.19 and additional references]
weak and vague convergence, Prohorov distance
25.04.16Transport plans and convergence in measureTania Kosenkova[Shioya Def 1.20-Lemma 1.27]
(Sub-)transport plan, Ky-Fan metric
02.05.16Levy's isoperimetric inequalityTania Kosenkova[Shioya 2.1]
Maxwell-Boltzmann distribution law, normal law a la Levy
09.05.16mm-spaces and Levy familiesElke Rosenberger[Shioya 2.2-2.3]
Lipschitz order, observable diameter
23.05.16Separation distanceSara Azzali[Shioya 2.4 plus Thm 2.31 without proof and Lemma 2.32 with proof]
Relation between separation distance and observable diameter, Levy-Gromov isoperimetric inequality
30.05.16Manifolds with positive Ricci curvaturePhillip Thonke[Shioya 2.5]
Bounds for observable diameter, more examples of Levy families
13.06.16Spectrum of the LaplacianMatthias Ludewig[Shioya 2.6]
Eigenvalue estimates in terms of separation distance
20.06.16Hausdorff distanceFlorian Hanisch[Shioya, 3.1]
27.06.16Gromov-Hausdorff distanceFlorian Hanisch[Shioya 3.2]

Literatur:

Takashi Shioya: Metric measure geometry, EMS 2016