Seminars, 2015

Lectures:
  • January 27, 2015
    Neumann Domains
    Prof. Ram Band, Department of Mathematics, Technion

    Abstract
    A Laplacian eigenfunction on a two-dimensional manifold dictates some natural partitions of the manifold; the most apparent one being the well studied nodal domain partition. 
    An alternative partition is revealed by considering a set of distinguished gradient flow lines of the eigenfunction - those which are connected to saddle points. 
    These give rise to Neumann domains (a.k.a Morse-Smale complexes). We define Neumann lines and Neumann domains and present their fundamental topological properties.
    These in turn allow to discuss some aspects of counting the number of Neumann domains, giving estimates on their geometry and connecting them to the 'usual' nodal domains.
    The talk is based on joint works in progress with David Fajman, Peter Kuchment, Mark Dennis and Alexander Taylor.
  • January 20, 2015
    Boundedness and unboundedness of the first eigenvalue of the Laplacian
    Prof. Lev Buhovski, Tel Aviv University

    Abstract
    I will talk about a certain topic related to the first eigenvalue of the Laplace-Beltrami operator on Riemannian manifolds. This topic was inspired by the beautiful theorem of Hersch about the first eigenvalue of the Laplacian on a Riemannian 2-sphere.