Sara Farinelli

Nodal domains of eigenfunctions in singular spaces with synthetic Ricci curvature bounds

In the last decade there has been a growing interest in the study of geometric and analytical properties of metric measure spaces satisfying synthetic Ricci curvature bounds. However very little is known about properties and regularity of nodal sets of eigenfunctions of the Laplace operator.    
In this seminar we first give an introduction to spaces with synthetic Ricci curvature bound. Then we present a version of the Plejel-Courant nodal domain theorem in this setting.