The workshop will feature 3 minicourses held by senior speakers, 12 talks held by junior speakers, selected among participants, and one poster session. Every supported participant who is not giving a talk is very much expected to present a poster describing her or his research interests.
Title: The geometric Bogomolov conjecture
Abstract: I shall describe the content of the Bogomolov conjecture in Diophantine geometry (now a theorem of Ullmo and Zhang), and its geometric version over function fields. Then, I shall explain the main ideas to solve the geometric conjecture in characteristic zero. Keywords are: abelian varieties, canonical heights, small points, but also foliations, holonomy, and equidistribution of orbits in dynamical systems. I shall explain the meaning of all these notions, and how they interact in the context of the Bogomolov conjecture.
Title: Fano manifolds and birational geometry.
Abstract: We will illustrate some of the techniques in birational geometry and the Minimal Model Program in the framework of Mori dream spaces, and their applications to the study of (smooth, complex) Fano manifolds, with a particular focus to dimension 4. A tentative schedule:
- 1st lecture: Mori dream spaces and birational geometry; examples
- 2nd lecture: overview on Fano varieties and their properties as Mori dream spaces
- 3rd lecture: the Lefschetz defect of Fano varieties, properties and study via birational geometry
- 4th lecture: geometry of Fano 4-folds with large second Betti number.
Title: The monodromy of projective holomorphic symplectic varieties and its significance.
Abstract: We will review the role the monodromy group plays in the Torelli theorem, the structure of the ample and movable cones, and the study of algebraic cycles on projective holomorphic symplectic varieties.