Vorträge in der Woche 24.10.2022 bis 30.10.2022
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Donnerstag, 27.10.2022: Causal Structure at Infinity and the Positive Mass Theorem
Peter Cameron (University of Edinburgh)
A spacetime is said to satisfy the Penrose property if every pair of points on past and future null infinity can be connected by a timelike curve. Penrose showed that this property fails in Minkowski spacetime of any dimension but is satisfied in 3+1 dimensional positive mass Schwarzschild. I will consider the Penrose property in more detail and discuss how it is related to the ADM mass and dimensionality of the spacetime. I will then show how some of the ideas arising in the study of this property can be used to prove a version of the positive mass theorem. Finally, I will discuss how the apparent failure of the Penrose property in higher dimensions (regardless of the ADM mass) may be linked to the greater regularity of possible conformal completions of the spacetime at spacelike infinity.
| Uhrzeit: | 14:00 - 15:30 |
| Ort: | S 9 (C 06 H 05) und über Zoom. Den Zoom-Link erhalten Sie per E-Mail von Frau Martina Jung oder Frau Martina Neu. |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Prof. Dr. Carla Cederbaum, Dr. Melanie Graf, Prof. Dr. Gerhard Huisken, Prof. Dr. Jan Metzger (Potsdam) |
Donnerstag, 27.10.2022: Quantum diffusion and related questions
Dr. Mitia Duerinckx (Université Libre de Bruxelles)
In this talk, we discuss a spectral perspective on the quantum diffusion conjecture for a quantum particle in a weakly random medium. We also draw the link to the study of Cherenkov radiation or friction effects for several translation-invariant QFT models that describe a non-relativistic quantum particle interacting with a quantized relativistic field of bosons. By a suitable fibration, those different problems are reduced to the metastability of the embedded mass shell of the free quantum particle, which is then naturally handled by means of Mourre's commutator method. However, regularity issues are known to be inherent to QFT models, due to their infinite dimensionality, thus challenging the application of Mourre's method. We introduce a non-standard construction of Mourre conjugate operators, which differs from second quantization. This leads us to several new results — although our findings remain partial in case of quantum diffusion. This is based on joint work with C.Shirley.
| Uhrzeit: | 16:00 |
| Ort: | C3N14 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |