The talk is divided in 2 parts, each roughly 45mn with a short break between. The 1st part is for more general audience and the 2nd part is more specialized.

Venue: for in-person attendees (Leonardo da Vinci, Luigi Stasi seminar room).

For virtual attendees:
https://zoom.us/meeting/register/tJEodeyspjooE9RLusdnk-qwB3tk0VcT8kuM
After registering, you will receive a confirmation email containing information about joining the meeting.

Part 1: Introduction to birational geometry and the Minimal Model Program
The Minimal Model Program is an important framework in the classification of projective varieties up to birational equivalence. In the talk, I plan to give an accessible introduction to the subject and describe some recent advances in the theory.

Part 2: Gale duality, blowups and moduli spaces
The Gale correspondence provides a duality between sets of n points in projective spaces P^s and P^r when n=r+s+2. For small values of s, this duality has a remarkable geometric manifestation: the blowup of P^r at n points can be realized as a moduli space of vector bundles on the blowup of P^s at the Gale dual points. We explore this realization to describe the birational geometry of blowups of projective spaces at points in very general position. We will focus in particular on the cases where the blowup fails to be a Mori Dream Space, reporting on a joint work with Carolina Araujo, Ana-Maria Castravet and Inder Kaur.