Vorträge in der Woche 22.04.2024 bis 28.04.2024

Montag, 22.04.2024: Comptutational methods and domain knowledge on the space of probability measures

Prof. Dr. Stephan Eckstein

The talk will give an overview of my recent and planned research, with the overarching theme being the efficient use of data, computational power and domain knowledge within probabilistic settings. Emphasis will be given to the frequently used probabilistic tool of optimal transport, which gives rise to a metric structure on the set of probability measures and is used in diverse areas related to data science. Motivated by applications in compression theory and causal inference, recent results on computational tractability of optimal transport, as well as suitably incorporating domain knowledge into optimal transport, are presented.

Donnerstag, 25.04.2024: A scattering construction for nonlinear wave equations on Kerr-Anti de Sitter spacetimes

Gemma Hood (Imperial College London)

Given the sharp logarithmic decay of linear waves on the Kerr-AdS black hole (Holzegel, Smulevici '13), it is expected that the Kerr-AdS spacetime is unstable as a solution of the Einstein vacuum equations. However, the scattering construction presented here for exponentially decaying nonlinear waves on a fixed Kerr-AdS background serves as a first step to confronting the scattering problem for the full Einstein system. In this context, one may hope to derive a class of perturbations of Kerr-AdS which remain 'close' and dissipate sufficiently fast.

Donnerstag, 25.04.2024: Exponential bounds of the condensation for dilute Bose gases

Dr. Simone Rademacher (LMU)

Bose-Einstein condensation (BEC) is a special phenomenon of the thermal equilibrium of Bose gases at low temperatures where a macroscopic fraction of particles occupy a common one-body quantum state. We justify BEC for a class of dilute Bose gases where the number of particles outside of the condensation is controlled in a rather strong sense. More precisely, we consider $N$ bosons on the unit torus $\Lambda=[0,1]^3$ in the Gross-Pitaevski regime where the interaction potential scales as $N^2 V(N(x-y))$. We prove that the thermal equilibrium at low temperatures exhibits BEC in a strong sense, namely the probability of having n particles outside of the condensation decays exponentially in n. This is joint work with Phan Thanh Nam.

Freitag, 26.04.2024: Plancherel Convergence and Zeta Functions

Claudius Kamp