Samuel Boissière: "DIVISORIAL CONTRACTIONS TO CODIMENSION THREE ORBITS" (SLIDES)

Abstract. I will present some recent results obtained in collaboration with Enrica Floris on the description of high dimensional equivariant divisorial contractions with nice geometric properties.

Ana-Maria Castravet, Antonio Laface: "BLOWN-UP TORIC SURFACES WITH NON-POLYHEDRAL EFFECTIVE CONE - I (SLIDES) AND II (SLIDES)"

Abstract. We will discuss examples of projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudoeffective cone. As a consequence one can show that the pseudoeffective cone of the Grothendieck-Knudsen moduli space \bar{M}_{0,n} is not polyhedral for n >= 10. The talk is in two parts: The first part will focus on the connection between the Grothendieck-Knudsen moduli spaces \bar{M}_{0,n} and blow-ups of toric varieties, as well as introducing a special class of polygons, which give rise to projective toric surfaces whose blow-up at a general point has a non-polyhedral pseudoeffective cone in characteristic zero. The second part will focus on results in positive characteristic.

This is joint work with J. Tevelev and L. Ugaglia.

Eleonora Anna Romano: "TORUS ACTIONS AND BIRATIONAL GEOMETRY" (SLIDES)

Abstract. In this talk we focus on complex, smooth, projective varieties admitting a non-trivial C^*-action. We introduce a new approach to investigate such varieties, using instruments coming from birational geometry. In particular, we relate small bandwidth varieties with Atiyah flips and special Cremona transformations. We report recent classification results of small bandwidth varieties, with particular attention to the case of bandwidth 3. We finally discuss some applications, in the framework of LeBrun-Salamon conjecture.

This is a joint project with G. Occhetta, L. Solá Conde and J. Wiśniewski.