Vorträge

Mittwoch, 19.11.2025: Quadratically enriched plane curve counting via tropical geometry

Felix Röhrle (Tübingen)

Consider the classical problem in enumerative geometry of counting rational plane curves through a fixed configuration of points. The problem may be considered over any base field and the point conditions might be scheme theoretic points. Recently, Kass--Levine--Solomon--Wickelgren have used techniques from $\mathbb{A}1^^1^$-homotopy theory to define an enumerative invariant for this problem which is defined over a large class of possible base fields. This new theory generalizes Gromov-Witten invariants (base field = complex numbers) and Welschinger invariants (base field = real numbers) simultaneously. In this talk I will present a tropical correspondence theorem, which allows to effectively compute these new invariants. This is joint work with Andrès Jaramillo-Puentes, Hannah Markwig, and Sabrina Pauli.

Donnerstag, 20.11.2025: TBA

Saradha Senthil-Velu

TBA

Donnerstag, 20.11.2025: TBA

Marcus Flook (ANU)

TBA

Dienstag, 25.11.2025: Schottky and quasi-Fuchsian groups, Hitchin representations and higher Teichmüller theory

Daniel Funck

Mittwoch, 26.11.2025: The 1-fold tropical Abel-Prym map

Giusi Capobianco (Roma Tor Vergata)

The algebraic Abel-Prym map relates the geometry of a double cover of algebraic curves with their corresponding Prym varieties. Birkenhake and Lange proved that the map has degree 2 if and only if the source curve is hyperelliptic. In the talk I will present joint work with Yoav Len, in which we investigate the 1-fold Abel-Prym map in the tropical setting and prove similar results. I will show that the tropical Abel-Prym map is a harmonic morphism of degree 2 if and only if the source graph is hyperelliptic. Furthermore, I will prove that the Jacobian of the image of this map is isomorphic, as pptav, to the Prym variety of the cover and relate this result to the tropical bigonal construction.

Donnerstag, 27.11.2025: TBA

Simone Coli (Universität Tübingen)

TBA

Donnerstag, 04.12.2025: TBA

Dr. Ahmed Ellithy (Uppsala University)

TBA

Donnerstag, 11.12.2025: Rigidity aspects of a singularity theorem

Carl Rossdeutscher (Universität Wien)

In 2018 Galloway and Ling established the following cosmological singularity theorem: If a (3+1)-dimensional spacetime satisfying the null energy condition contains a compact Cauchy surface with a positive definite second fundamental form (i.e., it’s expanding in all directions), then the spacetime is past null geodesically incomplete unless the Cauchy surface is a spherical space. We present some rigidity results for this singularity theorem. In particular if the second fundamental form is only positive semidefinite and the spacetime is past null geodetically complete, we show that the Cauchy surface (or at least a finite cover thereof) is a surface bundle over the circle with totally geodesic fibers or a spherical space. Under certain additional assumptions on the Cauchy surface, we show that passing to a cover is unnecessary. Our results make in particular use of the positive resolution of the virtual positive first Betti number conjecture by Agol. If a spacetime admits a U(1) isometry group, we can relax the assumption on the second fundamental form further.

Montag, 12.01.2026: tba

Stefan Friedl

Freitag, 30.01.2026: TBA

PhD Brian Harvie (Universität Kopenhagen)

TBA

Freitag, 30.01.2026: TBA

PhD Brian Harvie (Universität Kopenhagen)

TBA

Freitag, 30.01.2026: TBA

Olivia Vicanek Martinez (Universität Tübingen)

TBA

Freitag, 30.01.2026: TBA

Profl Dr. Uwe Semmelmann (Universität Stuttgart)

TBA