CONNECT

# Inverse Problems and Analysis

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Want to suggest a speaker? Send an email to Mahya Ghandehari.

Seminars will be held on Tuesdays from 11:00 am - 12:00 pm in Ewing 336.

Information about the Courtyard Newark - University of Delaware Hotel

 Dr. Nico Spronk, University of Waterloo Dr. Nico Spronk, University of Waterloo EWG 336 Title: Traces on group C*-algebras Abstract: For a discrete group, the existence of a trace on its reduced C*-algebra is well-known and there has recently been intensive study around issues of its uniqueness. This leads to the question, for a locally compact group, of whether its reduced C*-algebra admits a trace. B. Forrest and M. Wiersma and I have shown that for a compactly generated group, the reduced C*-algebra admits a trace exactly when the group admits a closed normal amenable subgroup whose quotient admits an invariant neighbourhood -- we denote this class of groups by [Am]$^\text{[IN]}$. We study related conditions for general locally compact groups. We exhibit an example of an [Am]$^\text{[IN]}$-group which is not inner amenable, thereby observing that the class of inner amenable groups is not closed under extension. 11/28/2017 4:00:00 PM 11/28/2017 5:00:00 PM False Dr. Constanze Liaw, University of Delaware Dr. Constanze Liaw, University of Delaware EWG 336 Title: General Clark model for finite rank perturbations

Abstract: The unitary perturbations of a given unitary operator by finite rank d operators can be parametrized by d x d unitary matrices; this generalizes the rank d=1 setting, where the Clark family is parametrized by the scalars on the unit circle. For finite rank perturbations we investigate the functional model of a related class of contractions, as well as a (unitary) Clark operator that realizes such a model representation for a particular contraction. We find a universal representation of the adjoint of the Clark operator, which features a matrix-valued Cauchy integral operator. By universal we simply mean that our formula is given in the coordinate free Nikolski–Vasyunin functional model. We express the matrix-valued characteristic functions of the model (for the class of contractions). In the case of inner characteristic functions results suggest a generalization of the normalized Cauchy transform to the finite rank setting. Parts of this talk is based on joint work with Sergei Treil. At least the first half of this talk will be accessible to graduate students. 12/8/2017 8:30:00 PM 12/8/2017 9:30:00 PM False