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 his research interests.
Title: Tropical and algebraic curves and their moduli spaces
Abstract: This will be a mini-course on tropical and algebraic curves and their moduli spaces, with an emphasis on the relationship between the two. Tropical geometry is a modern degeneration technique in algebraic geometry; it is a degeneration in which algebraic objects are replaced by entirely combinatorial ones. The theory of tropical curves is currently the one that has been fleshed out the most; we will use it as a window to look at applications of tropical geometry to enumerative and topological questions on algebraic curves and their moduli.
Title: Mumford-Tate groups and Motivic Galois groups
Abstract: In my lectures I will give an introduction to some abstract aspects of Hodge theory, an in particular to Mumford-Tate groups. In the first three lectures, I will introduce the basic definitions and will illustrate them with several concrete examples, for instance related to abelian varieties and K3 surfaces. In particular we will see how information about Mumford-Tate groups allows us to prove non-trivial results about algebraic cycles. Also the perspective of Tannakian categories will be discussed. In the last lecture, I plan to broaden the picture and compare Hodge theory with other cohomology theories; this lecture may be viewed as a first introduction to the theory of (pure) motives.
Title: Birational Geometry in positive characteristic.
Abstract: The goal of these lectures will be to give an overview of the recent results on the Minimal Model Program for varieties defined over an algebraically closed field of positive characteristic. In particular, we will focus on the relation between the singularities that appear in birational geometry, defined by proper birational morphisms, and the F-singularities, which are defined by the Frobenius morphism.