Vorträge in der Woche 05.02.2024 bis 11.02.2024
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Donnerstag, 08.02.2024: Homogeneous Ricci flows and the Dynamical Alekseevskii Conjecture
Robert de Santana Araújo (Universität Münster)
The Dynamical Alekseevskii Conjecture states that if a simply-connected homogeneous manifold is not contractible, then all homogeneous Ricci flow solutions on it have finite extinction time. Böhm showed that the conjecture is true for compact homogeneous spaces. In this talk, we will discuss the conjecture in the context of non-compact homogeneous spaces. In particular, I will present a structure result for the isometry group of non-compact homogeneous manifolds admitting an immortal Ricci flow solution. We will also discuss the long-time behavior of Ricci flows on a special family of Ricci flow invariant homogeneous metrics called awesome metrics, where we show the conjecture to be true.
| Uhrzeit: | 14:00 |
| Ort: | N15 (C-Bau) and virtual via zoom, for zoom link please contact Martina Neu |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam) |
Donnerstag, 08.02.2024: An efficient discretization to simulate the solution of linear-quadratic stochastic boundary control problem
Dr. Abhishek Chaudhary (Uni Tübingen)
In the first part of the talk, we will explore a practical approach to discretizing a linear-quadratic control problem associated with a stochastic heat equation with a non-homogeneous Dirichlet boundary. This leads to a discrete version of Pontryagin's maximum principle, involving the discretization of a backward SPDE. Typically, solving the BSPDE equation requires simulating conditional expectations, but we will introduce a reformulation of the discrete optimality condition that eliminates the need for such simulations. Moving on to the second part of the talk, we will delve into the strong rate of convergence results. Moreover, we also discuss the challenges in analyzing errors, particularly due to the less smooth nature of the optimal control.
| Uhrzeit: | 16:15 |
| Ort: | S7 (C5H10) |
| Gruppe: | Oberseminar Numerik |
| Einladender: | Lubich, Prohl |