CONNECT

Archive: Inverse Problems and Analysis

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 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. Anna Mazzucato Dr. Anna Mazzucato TBA Title: Elliptic equations on polyhedra and applications to the FEM

Abstract: I will discussed well-posedness of boundary value/interface problems for elliptic equations on polyhedral domains in weighted Sobolev spaces. The well-posedness and regularity results can be used to construct graded meshes that yields optimal convergence rates for FEMs.

11/8/2017 4:00:00 PM 11/8/2017 5:00:00 PM False Dr. Judith Packer, University of Colorado at Boulder Dr. Judith Packer, University of Colorado at Boulder EWG 336 Title: Wavelets associated to representations of graph C*-algebras Abstract: Here we discuss notions of wavelets defined on $L^2$-spaces for fractal-like sets associated to certain representations of graph C*-algebras and higher-rank graph C*-algebras, where the graphs in question are finite and strongly connected. Generalizing work of M. Marcolli and A. Paolucci, we obtain wavelets using the isometries and partial isometries generating the C*-algebras in question, coming from the graph relations. We also discuss some related spectral triples. This work is joint with C. Farsi, E. Gillaspy, A. Julien, and S. Kang. 10/31/2017 3:00:00 PM 10/31/2017 4:00:00 PM False Dr. David Shuman, Macalester College Dr. David Shuman, Macalester College EWG 336 Title: Dictionary design for graph signal processing Abstract: By transforming data into a new domain, techniques from statistics and signal processing such as principle components analysis and Fourier, wavelet, time-frequency, and curvelet transforms can sparsely represent and reveal relevant structural properties of time series, audio signals, images, and other data that live on regular Euclidean spaces. Such transform methods prove useful in compression, denoising, inpainting, pattern recognition, classification, and other signal processing and machine learning tasks. Unfortunately, naively applying these “classical” techniques to data on graphs would ignore key dependencies arising from irregularities in the graph data domain, and result in less informative and less sparse representations of the data. A key challenge in graph signal processing is therefore to incorporate the graph structure of the underlying data domain into dictionary designs, while still leveraging intuition from classical computational harmonic analysis techniques. In this talk, I will motivate the dictionary design problem for graph signals, examine some recently proposed dictionaries for graph signals, and discuss open issues and challenges. 10/24/2017 3:00:00 PM 10/24/2017 4:00:00 PM False