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Archive : Inverse Problems and Analysis

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Prof. Lixin Shen, Syracuse UniversityProf. Lixin Shen, Syracuse UniversityEWG336<br> Title: Structured Sparsity Promoting Functions and Proximity Algorithms<br><br>Description: This talk is divided into two parts. In the first part, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions and their Moreau envelopes. Properties of these functions are discussed by leveraging their structures. In particular, we provide sparsity guarantees for the general family of functions. We further study the behavior of the proximity operators of several special functions including indicator functions of closed convex sets, piece-wise quadratic functions, and the linear combinations of them. In the second part, we first give an overview of proximity operators and their essential properties. We then present our work on proximity algorithms for a class of optimization problems arising from image processing. 12/5/2018 6:30:00 PM12/5/2018 7:30:00 PMFalse
Prof. Volker Runde, University of Alberta Prof. Volker Runde, University of AlbertaEWG 336Title: What is amenability - from the Banach-Tarski paradox to Banach algebras <br><br> Abstract: We give a survey of how the notion of amenability emerged from John von Neumann's work on measure theory, and how it moved from there to abstract harmonic analysis, Banach and operator algebras.11/14/2018 6:30:00 PM11/14/2018 7:30:00 PMFalse
Dr. Shihua Gong, Penn State UniversityDr. Shihua Gong, Penn State UniversityEWG 336Title: Hybridized Mixed Finite Element Methods for Linear Elasticity and Optimal Multilevel Solvers <br><br> Abstract: Mixed finite element methods are important in solid mechanics since they avoid locking and provide a straightforward approximation for the stress, which is a symmetric tensor. The relevant existing conforming mixed finite element spaces for the symmetric stress are subject to continuity constraints at the element vertices, which is not natural for H(div) conformity and prohibits techniques like hybridization. This talk will relax the continuity at the element vertices and characterize the full special space for the stress. By this enrichment, the corresponding mixed finite element method is stable in some lower order cases. Moreover, hybridization techniques and multilevel solvers can be applied to solving the arising linear system.11/9/2018 4:00:00 PM11/9/2018 5:00:00 PMFalse
Dr. Murat Akman, University of Connecticut Dr. Murat Akman, University of Connecticut EWG 336<br> Title: Perturbations of elliptic operators on domains with non-smooth boundaries <br><br> Abstract: In this talk, we study perturbations of elliptic operators on domains with rough boundaries. In particular, we focus on the following problem: suppose that we have ``good estimates'' for the Dirichlet problem for a uniformly elliptic operator $L_0$, under what optimal conditions, are those good estimates transferred to the Dirichlet problem for uniformly elliptic operator L which is a ``perturbation'' of L_0? <br> We prove that if discrepancy between L_0 and L satisfies certain smallness assumption then the elliptic measure corresponding to L is in the reverse H{\"o}lder class with exponent 2 with respect to the elliptic measure corresponding to $L_0$ when the domain is 1-sided NTA satisfying the capacity density condition (CDC). <br> This is a joint work in progress with Steve Hofmann, Jose Maria Martell, and Tatiana Toro.10/24/2018 5:30:00 PM10/24/2018 6:30:00 PMFalse

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