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: Boosts of the STCMC Center of Mass

Saradha Senthil-Velu (Universität Tübingen)

In this talk, we will briefly review definitions of center of mass and angular momentum for asymptotically Euclidean initial data sets. The focus is the behavior of the spacetime constant–mean–curvature (STCMC) center under boosts. After clarifying boost notions and motivating the physically correct one for charge evolution, we will see that in model graphical cases in Schwarzschild the STCMC center transforms exactly as expected, in contrast to the constant–mean–curvature (CMC) center. Beyond this model class, we establish the linearized boost law for infinitesimal boosts of the STCMC center. Altogether, the STCMC center fits naturally into the asymptotic Poincaré structure of the ambient spacetime: it transforms correctly under boosts without imposing strong Regge–Teitelboim parity conditions, only weaker decay/parity hypotheses.

Donnerstag, 20.11.2025: Mean curvature flow analogues in Cauchy-Riemann (CR) Geometry

Marcus Flook (ANU)

In this talk, I will introduce and motivate Cauchy-Riemann (CR) geometry by considering real hypersurfaces embedded in complex Euclidean space. Firstly, I will discuss progress on both Darboux- and Alexandrov-type theorems in this setting. Secondly, I will introduce flows of CR hypersurfaces that are analogous to the mean curvature flow. Alongside the standard degeneracy due to tangential diffeomorphisms, such flows have an additional degeneracy due to the CR structure which will be discussed. Finally, I will discuss joint research with Ben Andrews on new flows which preserve key components of the CR structure.

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.

Donnerstag, 11.12.2025: TBA

Xabier Oianguren-Asua (Tübingen)

Montag, 12.01.2026: tba

Stefan Friedl

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