# Joint Seminar

The “Joint Seminar in Algebraic and Complex Geometry” is a research seminar, organized by the research groups in Basel, Freiburg, Nancy, Saarbrücken and Strasbourg. The seminar meets once or twice per semester in Strasbourg, for a full day. There are about four talks per meeting, both by invited guests and by speakers from the organizing universities. We aim to leave ample room for discussions and for a friendly chat.

The talks are open for everyone. Contact one of the organizers if you are interested in attending the meeting. We have some (very limited) funds that might help to support travel for some junior participants.

## Next Meeting

#### Date

November 15, 2019.

#### Venue

Institut de Recherche Mathématique Avancée
7 rue René Descartes
67084 Strasbourg Cedex
France

A description of the way is found here.

#### Speakers, Titles, Abstracts

• 10:30 – 11:30, Ariyan Javanpeykar (Mainz):
Dynamics of varieties with only finitely many rational points

We present recent work with Junyi Xie in which we show that a variety over a number field with only finitely many rational points in any given number field has only finitely many dominant rational self-maps. This result is motivated by Lang-Vojta’s conjecture. Indeed, such varieties should be of general type. We also prove similar results about varieties for which moduli spaces of maps from curves are bounded.

• 11:45 – 12:45, Giulia Saccà (Columbia):
Birational geometry of the intermediate Jacobian fibration
A few year ago with Laza and Voisin we constructed a hyperkähler compactification of the intermediate Jacobian fibration associated to a general cubic fourfold. In this talk I will first show how such a compactification $J(X)$ exists for any smooth cubic fourfold X and then discuss how the birational geometry of the fibration $J(X)$ is governed by extra algebraic cohomology classes on $X$.

• 14:45 – 15:45, Zsolt Patakfalvi (EPFL):
On the Beauville-Bogomolov decomposition in positive characteristic

I will present a work in progress joint with Maciej Zdanowicz towards a positive characteristic version of the Beauville-Bogomolov decomposition. Over the complex numbers this decomposition was shown using differential geometry methods in the 70’s and the 80’s. It concerns varieties with trivial canonical bundle, which we call K-trivial here. The main statement over the complex number is that smooth projective K-trivial varieties admit an étale cover which splits as a product of three types of varieties: abelian, Calabi-Yau and symplectic. I will present a similar statement in positive characteristic for (weakly) ordinary K-trivial varieties, the proof of which uses purely positive characteristic methods.

• 16:00 – 17:00, Mihai Păun (Bayreuth)
Subharmonicity of direct images and applications
We will present a few recent results obtained in collaboration with F. Campana and J. Cao. The main application concerns stable foliations with trivial first Chern class on compact Kähler manifolds.

## Mailing List

The meetings of the seminar will be announced via a mailing list. To subscribe, simply send an e-mail to seminar-nfs-subscribe@math.uni-freiburg.de.