Vorträge in der Woche 27.04.2026 bis 03.05.2026

Dienstag, 28.04.2026: From Welschinger to quadratically-enriched invariants: how broccoli invariance propagates to quadratically enriched tropical counts

Yanis Hedjem (Paris)

Jaramillo Puentes, Markwig, Pauli and Röhrle have recently defined a tropical multiplicity valued in the Grothendieck–Witt ring GW(k) of a field k of characteristic different from 2. When the point conditions are vertically stretched, this multiplicity factors over the vertices of a floor diagram, yielding a quadratically enriched count of rational tropical curves through r simple and s double point conditions. This count depends, a priori, on the merge positions: which pairs of adjacent simple points have been grouped into double points. The goal of this talk is to show that the dependence is illusory, uniformly in the Newton polygon (smooth del Pezzo), in the field k, and in the extensions d_1, ..., d_s. The argument is purely tropical and uses no correspondence theorem. The key idea is a transfer principle: the potential merge defect, which a priori lives in GW(k), is reduced to an integer linear combination — with coefficients independent of the field — of two canonical classes. It then suffices to specialise to k = R, where Göttsche–Schroeter's broccoli invariance forces the relevant integer coefficient to vanish; a standard annihilation identity in the Grothendieck–Witt ring then closes the argument over an arbitrary field. I will outline the general strategy of the proof and then explain what it implies « philosophically » about these new invariants.

Donnerstag, 30.04.2026: Mass aspect, MOTS and positive mass theorems for ALH manifolds

Prof. Greg Galloway (University of Miami)

In work with P. Chrusciel, L. Nguyen and T.-T. Paetz (CQG, 2018), a positive mass theorem was obtained for asymptotically locally hyperbolic (ALH) manifolds with boundary, having a toroidal end. The proof made use of properties of marginally outer trapped surfaces (MOTS), in addition to a key result concerning the mass aspect of ALH manifolds.  Here we present some new PMT results for ALH manifolds with toroidal ends, but without boundary, which allow for other more general ends.  The proofs, while still MOTS-based, involve a more elaborate technique (related to $\mu$-bubbles) introduced in work of D. A. Lee, M. Lesourd, and R. Unger (Calc. Var., 2023) in the AF setting. This talk is based on joint work with Tin-Yau Tsang.

Donnerstag, 30.04.2026: Landmarks in the History of Iteration Methods

Prof. Gerhard Wanner (Universität Genf)