KASS-seminarium

Abstrakt finns enbart på engelska: In Geometric Invariant Theory (GIT), the Hilbert-Mumford criterion gives a necessary and sufficient condition to find zeroes of a moment map. The famous Kobayashi-Hitchin correspondence can be interpreted as the Hilbert-Mumford criterion on an infinite dimensional space. It states that the Hermitian Yang-Mills equation (whose solutions can be seen as zeroes of a moment map) admits a solution if and only if an algebraic criterion is verified: the slope stability. In this talk, we will see a local version of the Hilbert-Mumford criterion in finite dimension and how it can be used to study perturbed geometric PDEs thanks to the Kuranishi theory.