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.
| Uhrzeit: |
10:15 - 11:15 |
| Ort: |
S10 |
| Gruppe: |
Oberseminar Kombinatorische Algebraische Geometrie |
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.
| Uhrzeit: |
14:00 |
| Ort: |
Seminarraum C4H33 and virtual via zoom, for zoom link please contact Martina Neu |
| Gruppe: |
Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie |
| Einladender: |
Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam) |
