Évènements

I will talk about the problem of determining the birational complexity of moduli spaces of curves and K3 surfaces. I will recall some recently introduced invariants that measure irrationality and talk about what is known for these moduli spaces. In the second half I will report on joint work with D. Agostini and K.-W. Lai, where we study how the degrees of irrationality of the moduli spaces of polarized K3 surfaces grow with respect to the genus g. We provide polynomial bounds. The proof relies on Kudla’s modularity conjecture for Shimura varieties of orthogonal type. For special genera we explot the deep Hodge theoretic relation between K3 surfaces and special hyperkähler fourfolds to obtain much sharper bounds.

Paracausal deformations of Lorentzian metrics and their consequences in quantum field theory

It is well-known that the space of Riemannian metrics on a smooth manifold is path-connected. Indeed, the convex combination of Riemannian metrics produces a Riemannian metric. This is not true, for the space of Lorentzian metric and a natural question pop up: Are there some natural operations that can be used to produce Lorentzian metrics starting from Lorentzian metrics?

This talk aims to provide sufficient conditions for some kind of linear combination of Lorentzian metrics to be a Lorentzian metric. In particular, the notion of paracausal deformation of a Lorentzian metric will be introduced and discussed in detail. After few characterizations, I will discuss shortly the consequences in quantum field theory.