Vorträge in der Woche 10.11.2025 bis 16.11.2025

Dienstag, 11.11.2025: Lattices, deformations and rigidity

Paul Vögele

Mittwoch, 12.11.2025: Enumerative Invariants of the Hirzebruch Surface F_n

Parisa Ebrahimian (Tübingen)

In the past two decades, tropical geometry has become a powerful modern tool for solving enumerative problems. In 2008, Hannah Markwig and Andreas Gathmann provided a tropical proof of the famous Kontsevich’s formula, making use of Mikhalkin’s correspondence theorem. In this talk, we present a further generalization of Kontsevich’s formula to the case of rational curves on the Hirzebruch surface F_n. Using Tyomkin’s correspondence theorem, which establishes the equality between algebraic and tropical counts of rational curves on toric surfaces satisfying point and cross-ratio conditions, we derive a recursive formula via tropical methods. This formula counts rational tropical curves of fixed degree in F_n that satisfy both point and multiple cross-ratio conditions, where the cross-ratio conditions here provide more flexibility than in previous works.

Donnerstag, 13.11.2025: Volume preserving mean curvature flow in asymptotically flat spaces

Jacopo Tena (Rome)

In this talk, I will discuss relations between curvature flows and foliations of asymptotically flat manifolds. Firstly, I will extend to the asymptotically flat setting a classical result by Huisken-Yau which allows one to construct a constant mean curvature foliation of the outer part of the manifold by an alternative approach to those by Nerz and Eichmair-Koerber. This is a joint work with C. Sinestrari. Secondly, I will provide an alternative construction of the constant spacetime-mean curvature foliation of an initial data set by Cederbaum-Sakovich by introducing a (volume preserving) fully nonlinear mean curvature flow whose speed takes into account the non-time-symmetric nature of the ambient.

Donnerstag, 13.11.2025: Boundary Superconductivity in BCS Theory

Dr. Barbara Roos (L'Aquila)

The connection between two important models of superconductivity, Bardeen-Cooper-Schrieffer (BCS) theory and Ginzburg-Landau (GL) theory is well-understood for systems without boundaries, where GL theory can be rigorously derived from BCS theory. GL theory is in particular used to model boundary superconductivity, however, a derivation of GL from BCS in the presence of boundaries is currently still out of reach. As a first step, we study BCS theory for systems with boundaries. In particular, I will discuss how the presence of a boundary influences the critical temperature.

Donnerstag, 13.11.2025: Large-scale response theory for gapless Fermi systems in low dimensions

Dr. Harman Preet Singh (Tübingen)

For a class of non-interacting, one-dimensional gapless systems of lattice fermions, we consider the density and current dynamical responses to a density-type perturbation with slow modulation in space and time, in the infinite volume and zero temperature limit. Furthermore, we consider the edge density and current responses for quantum Hall lattice systems on a cylinder. We prove the validity of the linear response for such quantities, thus justifying Kubo’s formula, which we evaluate explicitly solely in terms of the spectral data at the Fermi points, and of the profile of the perturbation. Finally, we present the extension to weakly interacting one-dimensional fermions. The proof of validity of linear response on the physically relevant time-scale relies on a precise analysis of the imaginary-time Duhamel series, and in particular on a cancellation for the scaling limit of the higher order correlation functions describing the nonlinear response, achieved by renormalisation group methods. Based on joint works with M. Porta and G. Scola.