Schedule

The workshop featured 3 mini-courses held by senior speakers, 12 talks held by junior speakers, selected among participants, and one poster session. Here is the full schedule including junior talk abstracts:

Senior Talks:

Enrica Floris

Title: Minimal model program on varieties with an action of a connected group

Abstract: The minimal model program is a series of elementary operations that to a projective variety associate a simpler birational model: a variety with numerically effective canonical divisor or a fibration whose fibres are Fano varieties (a Mori fibre space). In this mini-course we will be interested in the latter case. We are in this category for example if the variety we start with is covered by rational curves. The outcome of the minimal model program is not unique and two different Mori fibre spaces are connected by a sequence of elementary diagrams called Sarkisov program. The context of minimal model program turns out to be useful when studying properties of a connected algebraic group acting on a variety. Having such an action has strong consequences on the geometry of the variety, which for instance in this case cannot have ample canonical class. If the group is linear, the variety acted on is covered by rational curves. We will explain how the minimal model program is compatible with the action of the group and that there are Sarkisov programs compatible with the action of the group. We will then give applications to the study of connected algebraic subgroups of the Cremona group.

Dhruv Ranganathan

Title: Logarithmic and tropical moduli theory (notes)

Abstract: Logarithmic geometry is an incarnation of the theory of manifolds with corners within algebraic geometry. As a result, it has lots of things to say about compactification problems, especially in the context of moduli theory. An important insight of the last decade has been that tropical geometry gives rise to a simple calculus for manipulating logarithmic structures. I will try to illustrate this by giving you a tour of moduli problems from the logarithmic perspective, focusing on the logarithmic geometry of stable curves, stable maps, and the Hilbert scheme. We will run into a number of beautiful geometric ideas along the way including Chow quotients, matroids, Gröbner theory, and semistable reduction.

Giulia Saccà

Title: Hyper-Kähler manifolds and Lagrangian fibrations

Abstract: Compact hyper-Kähler manifolds are one of the building blocks of compact Kähler manifolds with trivial first Chern class and are the natural higher dimensional analogue of K3 surfaces. Lagrangian fibrations are the natural generalization of elliptic K3 surfaces. In these lectures I will give an introduction to hyper-Kähler manifolds with a focus on Lagrangian fibrations.

Junior Talks: