Michael Wemyss (Glasgow): The Homological MMP
Abstract: I will explain how, given a crepant morphism with one-dimensional fibres between 3-folds, it is possible to use noncommutative deformations to jump between minimal models in a satisfyingly algorithmic fashion. As part of this, a flop is viewed homologically as the solution to a universal property, and so is constructed not by changing GIT, but instead by changing the algebra in a cluster-like way. Carrying this extra information allows us to iterate, without having to calculate everything from scratch. Proving things in this way has many other consequences, and I will explain some of them, both theoretical and computational.