Schedule

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.

Please note that it will not be possible to print posters directly in Bucharest, since Monday 17 will be a public holiday. There are no restrictions on the size of the posters, but we recommend the standard A0.

On Thursday afternoon, Andrei Neguț (MIT) will give a talk in the IMAR Algebraic Geometry Seminar. It will be in the usual seminar room. All GAeL participants are welcome to attend!

Senior Talks:

Serge Cantat

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.

Notes in French for this lecture can be found here.

Cinzia Casagrande

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.

Notes written by Carlos Maestro Pérez for this course can be found here.

Eyal Markman

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.

The lecture notes of Cantat's course are available here.

IMAR Algebraic Geometry Seminar:

Andrei Neguț

Title: The Beauville-Voisin conjecture for Hilb(K3) and the Virasoro algebra

Abstract: We give a geometric representation theory proof of a mild version of the Beauville-Voisin Conjecture for Hilbert schemes of K3 surfaces, namely the injectivity of the cycle map restricted to the subring of Chow generated by tautological classes. Our approach involves lifting formulas of Lehn and Li-Qin-Wang from cohomology to Chow groups, and using them to solve the problem by invoking the irreducibility criteria of Virasoro algebra modules, due to Feigin-Fuchs. Joint work with Davesh Maulik.

The complete list of titles and abstracts is available here.