Schedule

The workshop will feature 3 mini-courses held by senior speakers, 12 talks held by junior speakers (selected among participants) and one poster session. There will be a social dinner.

Location of the talks: Collegezaal (lecture room) 3, Gorlaeus Lecture Hall

Schedule:

Senior Speakers:

• Olivier Benoist - École Normale Supérieure Ulm

  • Title: Stein spaces from an algebraic geometer's perspective

  • Abstract: Stein spaces are the complex-analytic analogues of affine algebraic varieties. Among them are all closed analytic subspaces of a Euclidean space. In this series of lectures, after a general introduction to their geometry, we will focus on questions concerning Stein spaces that have an algebro-geometric origin (arithmetic of their function field, Brauer group, cycles).

• Valentijn Karemaker - University of Amsterdam 

  • Title: Dieudonné theory

  • Abstract: The main result of Dieudonné theory provides an anti-equivalence between the category of p-divisible groups over a perfect field k of characteristic p, and the category of Dieudonné modules that are free of finite rank over the Witt vectors W = W(k). This implies that Dieudonné modules play an important role in understanding varieties, in particular abelian varieties, in characteristic p through their p-divisible groups. In addition, Oda proved that the Dieudonné module of the p-torsion group scheme of an abelian variety can be described in terms of its de Rham cohomology.

In this mini-course we will introduce Dieudonné modules and p-divisible groups, discuss their rich theories, explain the anti-equivalence between them, and explore applications to abelian varieties in characteristic p.

• Luca Schaffler - Roma Tre University

  • Title: Explicit geometry of moduli spaces of stable pairs

  • Abstract: Moduli spaces of smooth algebraic varieties are often non-compact: in families, varieties can degenerate, acquiring singularities or breaking into components. A proper (in fact projective) moduli space can be obtained by enlarging the moduli problem to stable pairs (X,D) allowing semi-log canonical singularities and requiring KX+ D to be ample. This is the Kollár–Shepherd-Barron–Alexeev (KSBA) compactification, the higher-dimensional analogue of the Deligne–Mumford–Knudsen compactification of the moduli space of pointed curves. In this series of lectures we introduce the basics of the KSBA framework, with a focus on surfaces. A guiding theme will be the explicit description of boundary strata in KSBA moduli spaces by computing stable limits of degenerating families, especially in the context of (weighted) line arrangements in P2 and stable surfaces (the case D=0).

Junior Speakers:

• Bilal Aytekin - University of Maryland

  • Title: TBA

  • Abstract: TBA

• Sophie Friesen - Leibniz University Hannover

  • Title: TBA

  • Abstract: TBA

• Gianluca Grassi - University of Ferrara

  • Title: TBA

  • Abstract: TBA

• Daniel Holmes - Institute of Science and Technology Austria

  • Title: TBA

  • Abstract: TBA

• Lucas Lagarde - Sorbonne Paris Nord University

  • Title: TBA

  • Abstract: TBA

• Isaac Martin - The University of Texas at Austin

  • Title: TBA

  • Abstract: TBA

• Enzo Pasquereau - Nantes University

  • Title: Combinatorial patchworking in higher codimension

  • Abstract: Combinatorial patchworking is a powerful tool used for constructing real algebraic hypersurfaces with controlled topology. It has led to signifcant advances including on the problem of the existence of maximal variety (the ones with the higher Betti numbers with respect to the Smith-Thom inequality).

I will present the combinatorial patchworking method originally due to Viro and then discuss generalizations to higher codimension. In particular, we give explicit patchworking rules similar to the formulation for hypersurfaces that allow to construct real complete intersections. As an application, we construct a families of pair of maximal surface and maximal curve in the real projective 3-space.

• Anna-Maria Raukh - University of Stavanger

  • Title: TBA

  • Abstract: TBA

• Davide Ricci - UVSQ Versailles University

  • Title: TBA

  • Abstract: TBA

• Francesca Rizzo - Paris Cité University

  • Title: On Hodge correspondences between Fano and Hyper-Kähler manifolds.

  • Abstract: Hyper-Kähler manifolds are among the fundamental building blocks in the Beauville–Bogomolov decomposition of compact Kähler manifolds with trivial first Chern class. Interestingly, all known examples of locally complete families of hyper-Kähler manifolds are related to Fano geometry. The first such example was studied by Beauville and Donagi, who showed that the Hilbert scheme parametrizing lines on a smooth cubic fourfold is a hyper-Kähler fourfold. Moreover, the associated incidence correspondence induces a Hodge isometry between the primitive middle cohomology of the cubic fourfold and the primitive second integral cohomology of its variety of lines.

We will discuss this example and explain how a similar phenomenon occurs for the other four known examples of projective families of hyper-Kähler manifolds. In particular, we will present some recent results on EPW cubes (hyper-Kähler sixfolds) and Gushel–Mukai sixfolds (Fano varieties).

• Sara Stephens - Cornell University

  • Title: TBA

  • Abstract: TBA

• Alice Villa - University of Bologna

  • Title: TBA

  • Abstract: TBA