Events for 02/23/2017 from all calendars

Linear Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Nicolas Matte Bon, ETH Zürich

Title: Chabauty dynamics and C*-simplicity of groups of homeomorphisms

Abstract: Let G be a countable group. The space of subgroups of G, endowed with the Chabauty topology, is naturally a compact space on which G acts continuously by conjugation. The talk will focus on the topological dynamics of this action, in particular on the study of its minimal invariant subsets (named uniformly recurrent subgroups). I will explain a method to study the uniformly recurrent subgroups of a class of groups of homeomorphisms, such as Thompson's groups and their relatives, some groups acting on rooted and non-rooted trees, topological full groups. I will discuss applications to the simplicity of the reduced C^*-algebra of these groups, linked to uniformly recurrent subgroups by results of Kennedy and Kalantar-Kennedy, and to rigidity-type results for non-free actions. This is a joint work with Adreian Le Boudec.

Mathematical Physics and Harmonic Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Graham Cox, Memorial University, Newfoundland

Title: Manifold decompositions and indices of Schrödinger operators

Abstract: When finding the eigenvalues of a differential operator, it is often convenient to partition the spatial domain and then compute the spectrum on each component. This is useful when the operator has localized structure, such as a compactly supported defect superimposed over a known background. In this case the partitioning effectively decouples the defect and the background. One must then determine how the spectrum on the original domain is related to the spectra on the subdomains.

I will describe such spectral decompositions using the Maslov index, a generalized winding number for paths of Lagrangian subspaces. Using a homotopy argument, I will show that the Morse index of the original boundary value problem is given by the sum of the Morse indices on each subdomain plus a “coupling term” that depends on the Dirichlet-to-Neumann maps for the common boundary. An immediate corollary is a new proof of Courant's nodal domain theorem, with an explicit formula for the nodal deficiency. I will also discuss applications to periodic boundary conditions. This is joint with Christopher Jones and Jeremy Marzuola at UNC Chapel Hill.