Vorträge in der Woche 17.10.2022 bis 23.10.2022
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Montag, 17.10.2022: Initial data sets: a Riemannian approach to general relativity
Dr. Armando Cabrera Pacheco (Tübingen)
A fundamental problem in general relativity is to understand the geometry of spacetimes, that is, solutions to the Einstein equations. When considering these equations as an initial value problem, the initial value corresponds to a Riemannian manifold together with a symmetric 2-tensor, called an initial data set. The study of isolated systems, like a collection of stars or black holes, naturally leads to the concept of asymptotically flat manifolds, an important class of initial data sets. In this talk, we will motivate and explain general properties of asymptotically flat initial data sets, mention important questions related to their geometry and describe some recent results motivated by those questions.
| Uhrzeit: | 17:15 - 18:15 |
| Ort: | N14 |
| Gruppe: | Kolloquium |
| Einladender: | Die Dozent:innen des Fachbereichs |
Mittwoch, 19.10.2022: Enumeration of tropical curves in abelian surfaces
Dr. Thomas Blomme (Université de Genève)
Tropical geometry is a powerful tool that allows one to compute enumerative algebraic invariants through the use of some correspondence theorem, transforming an algebraic problem into a combinatorial problem. Moreover, the tropical approach also allows one to twist definitions to introduce mysterious refined invariants, obtained by counting tropical curves with polynomial multiplicities. So far, this correspondence has mainly been implemented in toric varieties. In this talk we will study enumeration of curves in abelian surfaces and use the tropical geometry approach to prove a multiple cover formula that enables an simple and elegant computation of enumerative invariants of abelian surfaces.
| Uhrzeit: | 10:30 |
| Ort: | C4H33 |
| Gruppe: | Oberseminar Kombinatorische Algebraische Geometrie |
| Einladender: | Hannah Markwig |
Donnerstag, 20.10.2022: Recent Estimates on the Bartnik mass
Annachiara Piubello (University of Miami)
In this talk, we will discuss some recent estimates on the Bartnik mass for data with non-negative Gauss curvature and positive mean curvature. In particular, if the metric is round the estimate reduces to an estimate found by Miao and if the total mean curvature approaches 0, the estimate tends to 1/2 the area radius, which is the bound found by Mantoulidis and Schoen in the blackhole horizon case. We will then discuss some geometric implications. This is joint work with Pengzi Miao.
| Uhrzeit: | 14:00 - 15:30 |
| Ort: | S 9 (C 06 H 05) and virtual via zoom, for zoom link please contact Martina Jung or Martina Neu |
| Gruppe: | Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: | Prof. Dr. Carla Cederbaum, Dr. Melanie Graf, Prof. Dr. Gerhard Huisken (Tübingen), together with Prof. Dr. Jan Metzger (Potsdam) |
Donnerstag, 20.10.2022: Macroscopic dynamics for nonequilibrium biochemical reactions from a Hamiltonian viewpoint
Prof. Liu Jian-Guo (Duke University, USA)
Most biochemical reactions in living cells are open systems interacting with environment through chemostats to exchange both energy and materials. At a mesoscopic scale, the number of each species in those biochemical reactions can be modeled by a random time-changed Poisson processes. To characterize macroscopic behaviors in the large number limit, the law of large numbers in the path space determines a mean-field limit nonlinear reaction rate equation describing the dynamics of the concentration of species, while the WKB expansion for the chemical master equation yields a Hamilton–Jacobi equation and the corresponding Lagrangian gives the good rate function (action functional) in the large deviation principle. We decompose a general macroscopic reaction rate equation into a conservative part and a dissipative part in terms of the stationary solution to the Hamilton–Jacobi equation. This stationary solution is used to determine the energy landscape and thermodynamics for general chemical reactions, which particularly maintains a positive entropy production rate at a non-equilibrium steady state. The associated energy dissipation law at both the mesoscopic and macroscopic levels is proved together with a passage from the mesoscopic to macroscopic one. The existence of this stationary solution is ensured by the optimal control representation at an undetermined time horizon for the weak KAM solution to the stationary Hamilton–Jacobi equation. Furthermore, we use a symmetric Hamiltonian to study a class of non-equilibrium enzyme reactions, which leads to nonconvex energy landscape due to flux grouping degeneracy and reduces the conservative-dissipative decomposition to an Onsager-type strong gradient flow. This symmetric Hamiltonian implies that the transition paths between multiple steady states (rare events in biochemical reactions) is a modified time reversed least action path with associated path affinities and energy barriers.
| Uhrzeit: | 16:00 |
| Ort: | C3N14 |
| Gruppe: | Oberseminar Mathematical Physics |
| Einladender: | Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka |