Event

Moduli Spaces and Singularities Scientific Meeting

Monday, May 20, 2024toFriday, May 24, 2024

Overview

Moduli spaces parametrize certain mathematical objects such as the solutions to a partial differential equation or geometric structures on a given topological space. As such, they arise naturally in analysis, geometry, and mathematical physics. They often are themselves equipped with a natural geometric structure which is interesting in its own right. For instance, the moduli space of SU(2)-monopoles on R3 comes with a natural hyperKähler metric. Except in special cases, they are typically non-compact or singular, in which case a careful study of what is happening at infinity or near the singularity is crucial in understanding how the solutions or the geometric structures they parametrize can degenerate.

In the complex world, these issues are important in the compactification of the moduli spaces of K-stable (and Kähler-Einstein) Fano varieties in the light of recent results obtained from the algebro-geometric point of view. In a complementary direction, the moduli spaces of canonically polarized manifolds have recently been the subject of much attention: the question of the regularity of the potential of the Weil-Petersson metric leads to a new insight on the geometry of the moduli space of canonically polarized varieties.

Registration deadline: May 16, 2024

Participants should make their own lodging arrangements ahead of time and be cautious when contacted by third parties who suggest they are associated with the conference.