Vorträge in der Woche 17.06.2024 bis 23.06.2024

Dienstag, 18.06.2024: Abstract buildings

Parisa Ebrahimian

Mittwoch, 19.06.2024: Piecewise Polynomial Structure of (Twisted) Hurwitz Numbers

Veronika Körber (Tübingen)

The origin of Hurwitz numbers is in complex analysis, where they count covers of Riemann surfaces under certain conditions. Later on, it was found that these same numbers can be used to count tropical covers. When we treat the weights of the ends as variables, one can find a piecewise polynomial structure at the Hurwitz numbers. I studied the terms of lower degree in these polynomials, which can cancel in many cases.

Donnerstag, 20.06.2024: On ancient and eternal solutions to mean curvature flow

Dr. Alex Mramor ( University of Copenhagen )

In this talk we'll discuss some constructions of ancient solutions to the mean curvature flow, as well as a partial classification result for eternal flows of "finite total curvature type" in (Formel.

Donnerstag, 20.06.2024: Über die Sätze von Minding und Bernstein

Madeleine von Kuhlberg

Im Vortrag wird die kombinatorische Formel von D. Bernstein für die Anzahl gemeinsamer Lösungen des algebraischen Gleichungssystems in 2 Variablen nach der Methode von Minding begründet.

Donnerstag, 20.06.2024: Approximation of stochastic fluid models

Joern Wichmann ( Monash University Melbourne, Australia )

In this talk we discuss the design of algorithms in the context of stochastic fluid models. These models arise from classical deterministic ones, e.g. Stokes and Navier--Stokes, by enriching them with an additional stochastic forcing. This forcing accounts for random effects on micro-scales such as random movement of individual fluid particles. It introduces a particular challenge in the design of algorithms -- solutions possess limited regularity. The irregularity prohibits generalising deterministic algorithms and calls for robust algorithms adapted to the natural regularity of solutions. We present design principles that can cope with irregularities and discuss how to derive a rigorous mathematical error analysis. The talk is based on joint work with Kim-Ngan Le (Monash University).

Donnerstag, 20.06.2024: On Lieb-Robinson bounds for long-range interacting bosons

Jingxuan Zhang (Tsinghua University, PR China)

We prove a thermodynamically stable Lieb-Robinson bound (LRB) for bosons with long-range interaction on lattices. The condition is that the initial state admits (i) uniformly bounded density from above and (ii) no particle in the region separating the initial supports of the observables entering the LRB. Furthermore, if the initial state has controlled density from both above and below, then the validity threshold for decay rate of the hopping terms can be improved to $\alpha > d+ 2$. The proof is based on the weak LRBs and the thermodynamically stable bounds on particle transport obtained in recent joint works with Lemm, Rubiliani, and Sigal.

Freitag, 21.06.2024: Morse Theorie und eine Zerlegung von Mannigfaltigkeiten in Kreisscheiben

David Seez (Universität Tübingen)