Geometry Seminar

University of Tor Vergata, Department of Mathematics

24th of January 2023 14:30-15:30, room “Dal Passo”

Speaker

Antonio Trusiani

(Institut de Mathématiques de Toulouse)

Title

A relative Yau-Tian-Donaldson conjecture and stability thresholds

Abstract

In the first part of the talk the set of Kähler-Einstein metrics with prescribed singularities and a new relative K-stability notion will be introduced. A particular focus will be given to the motivations and intuitions, making a comparison with the log K-stability/log Kähler-Einstein metrics. The two notions mentioned above will then be related to each other through a Yau-Tian-Donaldson correspondence, which will be the core of the talk. An important role will be played by a valuative criterion, which can be also used to relate the prescribed singularities setting to the absolute setting. Indeed new estimates on the Fujita-Odaka δ-invariant and new information on the genuine K-stability will be deduced. Time permitting, a further discussion on some future developments will conclude the talk.