Vorträge in der Woche 29.01.2018 bis 04.02.2018
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Montag, 29.01.2018: Index theory on spacetimes
Prof. Dr. Christian Bär (Universität Potsdam)
Vorkolloquium um 16 Uhr (moderiert von Sophia Jahns): An introduction to the Atiyah-Singer index theorem <br>Abstract des Kolloquiumsvortrags: Starting with Atiyah and Singer's famous theorem, index theory for elliptic operators has grown into a very active area of mathematical research with numerous applications in fields such as geometry, topology, mathematical physics, and number theory. Index theory relates the solution space of a partial differential equation to geometric quantities of the underlying manifold. Usually, the existence of an index requires ellipticity of the differential operator. <br>On a curved spacetime, mathematically modeled by a Lorentzian manifold, the natural operators such as the Dirac operator are not elliptic but hyperbolic and hence show a totally different analytic behavior. It therefore came as a surprise that under certain reasonable conditions there is an index theorem in this case nonetheless. It has been applied to compute anomalies in quantum field theory. <br> In the talk I will explain this in more detail without becoming too technical. This is joint work with Alexander Strohmaier (Leeds University, UK).
| Uhrzeit: | 17:15 |
| Ort: | N 14 |
| Gruppe: | Kolloquium |
| Einladender: | Cederbaum, Huisken |
Dienstag, 30.01.2018: Beispiele von relativ gleichmäßig stetigen positiven Halbgruppen auf Vektorverbänden
M. Kaplan (Jlubljana)
Wir definieren relativ gleichmäßig stetige positive Halbgruppen auf Archimedischen Vektorvebänden und betrachten verschiedene Klassen von Koopman, Hitze und Black-Scholes Halbgruppen auf den Räumen der stetigen, gleichmäßig stetigen und Lipschitz-stetigen Funktionen.
| Uhrzeit: | 11:15 |
| Ort: | S10 |
| Gruppe: | Oberseminar Funktionalanalysis |
| Einladender: | R. Nagel |
Mittwoch, 31.01.2018: Die neue Kursstufe in Mathemaik: leistungsfach und Basisfach
StD Achim Pfeiffer (Spohn-Gymnasium Ravensburg)
Im Jahr 2021 legen erstmals Schülerinnen und Schüler in Baden-Württemberg das Abitur nach dem Besuch des Leistungs- oder Basisfaches ab. Über welche mathematischen Kenntnisse werden sie verfügen? Wodurch unterscheiden sich Leistungsfach und Basisfach? In dem Vortrag wird versucht, durch den Vergleich der Bildungspläne von Leistungsfach und Basisfach eine Antwort auf diese Fragen zu geben und die Intentionen der beiden Fächer zu erläutern.
| Uhrzeit: | 18:00 - 20:00 |
| Ort: | N14 |
| Gruppe: | AG Mathematik zwischen Schule und HochschuleG |
| Einladender: | Haug, Kölle, Loose, Schatz |
Donnerstag, 01.02.2018: Geometric Necks in Mean Curvature Flow
Felix Dietrich (Universität Tübingen)
Geometric necks arise as singularities of 2-convex solutions to mean curvature flow in Euclidian space. <br> We want to explain how to use the implicit function theorem to find a useful parametrization of these necks and how to follow this parametrization in time. Afterwards we talk about possible applications.
| Uhrzeit: | 14:15 |
| Ort: | S9 |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Cederbaum, Huisken |
Donnerstag, 01.02.2018: Quantitative logarithmic Sobolev inequalities and the Ricci flow
Jason Ledwidge (Universität Tübingen)
In this talk we will present a quantitative version of the logarithmic Sobolev inequality and stability results- known as the logarithmic Sobolev deficit - recently found by M.Fathi, E.Indrei and M.Ledoux. We will present the results on the Gauss space and mention how they can be generalised to weighted manifolds satisfying the Bakry- Emery Curvature dimension criterion. In order to prove these results, we will first show how to: obtain the logarithmic Sobolev inequality on Guass space; introduce the Curvature-Dimension criterion; and prove a famous transportation-cost inequality due to M.Talagrand. The proofs of these results will allow us (at least formally) to present Lojasiewicz inequalities (with optimal constants) on the 2-Wasserstein space. <br> Next, we will introduce G.Perelman's $\mathcal{F}$ and $\mathcal{W}$ functionals and show how they generalise the logarithmic Sobolev inequalitiy. We then discuss a potential way to generalise the results from the first part of the talk to this Ricci flow setting. Our hope is that these results will allow us to analyse the behaviour of 'almost' steady and shrinking gradient Ricci solitons. If time permits, we will state a gradient Lojasiewicz inequality for steady solitons due to Haslhofer-Mueller.
| Uhrzeit: | 15:15 |
| Ort: | S9 |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Cederbaum, Huisken |
Donnerstag, 01.02.2018: Interacting quantum field theories as relativistic statistical field theories of local beables
Dr. Antoine Tilloy (MPI für Quantenoptik, Garching)
I will present a generic method to construct collapse models with good symmetry properties starting from interacting quantum field theories. A peculiar feature of the resulting models is that they can be made empirically equivalent to the Standard Model supplemented with the Copenhaguen interpretation. Hence, whilst it solves the problem of finding relativistic collapse models, this approach hints at a reconsideration of the whole collapse program: as an interpretation or reformulation of QFT rather than as an extension making different predictions. This talk will be based upon arXiv:1702.06325
| Uhrzeit: | 16:15 |
| Ort: | N14 |
| Gruppe: | OS MaPhy |
| Einladender: | Hainzl, Keppeler, Porta, Teufel, Tumulka |