Oberseminar SoSe 24
Die Vorträge finden jeweils donnerstags um 16:45 Uhr im Raum WSC-N-U-3.05 (im Mathematikgebäude ) statt. Directions from the train station.
Der Tee findet ab 16:15 statt.
Alle Interessenten sind herzlich eingeladen!
The seminar takes place on Thursday, starting at 4:45pm. The duration of each talk is about 60 minutes.
Everybody who’s interested is welcome to join.
| 11.4.2024 | Yukako Kezuka (Paris) | Non-vanishing results for some CM elliptic curves |
| 18.4.2024 | Irene Spelta (Barcelona) | Special subvarieties of the Torelli locus: examples |
| 25.4.2024 | Alex Küronya (Frankfurt) | Structures on cohomology and P=W for abelian varieties |
| 2.5.2024 | N. N. | tba |
| 16.5.2024 | Mihai Pavel (Bukarest) | Variation of moduli of sheaves in higher dimensions |
| 23.5.2024 | Stefano Marseglia (University of French Polynesia) | tba |
| 6.6.2024 | – | reserviert |
| 13.6.2024 | Quentin Posva (Düsseldorf) | tba |
| 20.6.2024 | (Guido Kings, tbc) | tba |
| 27.6.2024 | – | Symposium Düsseldorf/Essen/Wuppertal |
| 4.7.2024 | Mario Kummer (TU Dresden) | tba |
| 11.7.2024 | Alexander Petrov (IAS) | tba |
| 18.7.2024 | Michael Thaddeus (Columbia) | tba |
Abstracts
Yukako Kezuka: Non-vanishing results for some CM elliptic curves
We prove non-vanishing results for the values at $s=1$ of the complex L-series of quadratic twists of the elliptic curves with complex multiplication introduced by B. Gross in his thesis. From this, we obtain the finiteness of their Tate–Shafarevich group. For a prime $\mathfrak P$ lying above the prime 2, we also prove a $\mathfrak P$-converse theorem in the rank 0 case for the higher-dimensional abelian varieties obtained by restriction of scalars.
Irene Spelta: Special subvarieties of the Torelli locus: examples
The Torelli morphism $j \colon \mathcal M_g \to \mathcal A_g$ associates to an algebraic curve $C$ its Jacobian $J_C$ (as a principally polarized abelian variety). Very classically, it is injective on geometric points. In this talk, we will discuss the interplay between the geometry of $\mathcal M_g$ and of $\mathcal A_g$. In particular, we will consider certain special subvarieties. We will explain how this is linked to a conjecture by Coleman and Oort, and we will analyse explicit examples.
Alex Küronya: Structures on cohomology and P=W for abelian varieties
The purpose of this talk is to discuss the significance of various extra structures on the (co)homology of algebraic varieties, leading to a discussion of the recent P=W conjecture and its verification for abelian varieties.
Mihai Pavel: Variation of moduli of sheaves in higher dimensions
We introduce a notion of semistability for coherent sheaves over a projective manifold, which is well-behaved from the perspective of variation in higher dimensions. Specifically, we obtain (new) moduli spaces of semistable pure sheaves, along with a locally finite wall-chamber structure that governs their variation with the change of semistability. This involves showing uniform boundedness statements for semistable pure sheaves.