Vorträge in der Woche 15.01.2024 bis 21.01.2024

Mittwoch, 17.01.2024: Universal polynomials for coefficients of tropical refined invariant in genus 0

Gurvan Mével ( Université de Nantes )

In enumerative geometry, some numbers of curves on surfaces are known to behave polynomially when the cogenus is fixed and the linear system varies, whereas it grows more than exponentially fast when the genus is fixed. In the first case, Göttsche's conjecture expresses the generating series of these numbers in terms of universal polynomials. Tropical refined invariants are polynomials resulting of a weird way of counting curves, but linked with the previous enumerations. When the genus is fixed, Brugallé and Jaramillo-Puentes proved that some coefficients of these polynomials behave polynomially, bringing back a Göttsche's conjecture in a dual and refined setting. In this talk we will investigate the existence of universal polynomials for these coefficients.

Donnerstag, 18.01.2024: Backward difference formulae for the transient Stokes problem: \\ optimal order velocity and pressure estimates

Balázs Kovács (Universität Paderborn)

In this talk we will present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. The numerical method uses backward difference formulae of order 1 to 6 in time and a wide class of Galerkin finite element methods. The main novelty of our approach lies in deriving optimal-order error estimates for \emph{both} the velocity and the pressure. The main issue, however, lies in the stability estimates for the saddle point problem. This will be shown using techniques which need no advertisement in Tübingen: Dahlquist’s $G$-stability theory together with the multiplier technique of Nevanlinna and Odeh (BDF1-6) and by Akrivis et al. (BDF6). The talk is based on joint work with Alessandro Contri and André Massing (NTNU).

Donnerstag, 18.01.2024: Lieb-Robinson bounds for a class of continuum fermions

Oliver Siebert (Uni Tübingen)

We establish a Lieb-Robinson bound for a d-dimensional continuous many-body fermionic system with an ultraviolet regularized pair interaction, as previously studied by M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims. Our proof is based on the ASTLO method and requires substantially less assumptions on the potentials. Furthermore, we also improve the associated one-body Lieb-Robinson bound to an almost ballistic one (i.e., an almost linear light cone). Finally, we discuss several applications, including the existence of a strongly continuous infinite-volume dynamics on the CAR algebra, the clustering of ground states in the presence of a spectral gap, and a fermionic continuum notion of conditional expectation. This is joint work with B. Hinrichs and M. Lemm.

Freitag, 19.01.2024: Grundideen der kausalen Inferenz

Clemens Teupe (Uni Tübingen)