Score matching for simulating sub-Riemannian diffusion bridge processes
De Karen Habermann
From gas giant planets to the spectral theory of subelliptic Laplacians
De Emmanuel Trélat
Apparaît dans la collection : Not Only Scalar Curvature Seminar
The behavior of the Yamabe invariant, as defined in Bernd Ammann’s previous lecture, differs strangely in dimension 4 from what is seen in any other dimension. These peculiarities not only manifest themselves in the context of the usual scalar curvature, but also occur in connection with certain curvature quantities that are built out of the scalar and Weyl curvatures. In this lecture, I will explain how the Seiberg-Witten equations not only allow one compute the Yamabe invariant for many interesting 4-manifolds, but also give rise to other curvature inequalities. I will then point out applications of these results to the theory of Einstein manifolds, while also highlighting related open questions that have so far proved impervious to these techniques.