Title: Interactions between contact topology, Riemannian geometry, and spectral theory
Speaker: Willi Kepplinger (University of Vienna)
Abstract:
It has long been recognized that there should be ''good ways'' of using Riemannian geometry in order to make progress in contact topology. In the first place, Riemannian geometry in general and geometric analysis in particular have had an incredible impact on the development of the field of low dimensional topology, and many people have hoped that the same would be true for contact topology as well. Various attempts have been made over the years to realize this hope but, except for a couple of notable results, strong connections have remained elusive. Nevertheless these few exceptions do show the promise of this approach, and the goal of my talk is to highlight some of these successes (some of which are quite recent) and to sketch some possible paths for future developments.
Talk given at the Prague-Hradec Králové seminar on Cohomology in algebra, geometry, physics and statistics:
www.math.cas.cz/index.php/events/event/3835
researchseminars.org/talk/PHK-cohomology-seminar/118/
The slides are available from:
users.math.cas.cz/~hvle/PHK/KepplingerContacttopology2024.pdf