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Archive : Inverse Problems and Analysis

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Priyanga GanesanPriyanga GanesanEWG 336Title: Quantum Majorization in Infinite Dimensions <br><br> Abstract:Majorization is a concept from linear algebra that is used to compare disorderness in physics, computer science, economics and statistics. Recently, Gour et al (2018) extended matrix majorization to the quantum mechanical setting to accommodate ordering of quantum states. In this talk, I will discuss a generalization of their concept of quantum majorization to the infinite dimensional setting. The entropic characterization of quantum majorization will be presented using operator space tensor products and duality . This is based on joint work with Li Gao, Satish Pandey and Sarah Plosker. <br><br>12/3/2019 6:00:00 PM12/3/2019 7:00:00 PMFalse
Prof. Kui Ren, Columbia UniversityProf. Kui Ren, Columbia UniversityEWG336Title: Inverse problems in photoacoustic imaging of nonlinear physics<br><br> Abstract: This talk will discuss inverse problems in the photoacoustic imaging of two-photon absorption of heterogeneous media where we intend to reconstruct coefficients in systems of semilinear diffusion and transport equations from single or multiple given data sets. We will present technical results but our goal is really to give an overview of recent developments on the modeling, computational and mathematical aspects of the problem. 11/19/2019 6:00:00 PM11/19/2019 7:00:00 PMFalse
Dr. Soumyashant Nayak, University of PennsylvaniaDr. Soumyashant Nayak, University of PennsylvaniaEWG336Title: Looking beyond the `algebra' in Murray-von Neumann algebras<br><br> Abstract: The set of closed densely-defined operators affiliated with a finite von Neumann algebra R has a natural *-algebraic structure and is called the Murray-von Neumann algebra associated with R. In the context of group von Neumann algebras, they play an important role in the study of $L^2$-invariants in geometry. On the algebraic side, they have been described as the Ore localization of finite von Neumann algebras (with respect to their multiplicative subset of non-zero-divisors) and studied for their nice ring-theoretic properties. In this talk, we will uncover some of their fundamental topological, order-theoretic and analytical aspects. This allows us to study abstract Murray-von Neumann algebras avoiding reference to a Hilbert space and messy `domain-tracking' arguments. As an application, we will use approximation techniques afforded by the intrinsic topology (which we call the $\mathfrak{m}$-topology, where `$\mathfrak{m}$' may be thought of as `measure' or `measure-theoretic') to transfer several standard operator inequalities for bounded self-adjoint operators to the setting of (unbounded) self-adjoint operators in Murray-von Neumann algebras.11/12/2019 6:00:00 PM11/12/2019 7:00:00 PMFalse
Dr. Yunan Yang, Courant Institute of Mathematical SciencesDr. Yunan Yang, Courant Institute of Mathematical SciencesEWG336Title: Analysis and Application of Optimal Transport For Challenging Seismic Inverse Problems<br><br> Abstract: In seismic exploration, sources and measurements of seismic waves on the surface are used to determine model parameters representing geophysical properties of the earth. Full-waveform inversion (FWI) is a nonlinear seismic inverse technique that inverts the model parameters by minimizing the difference between the synthetic data from the forward wave propagation and the observed true data in PDE-constrained optimization. The traditional least-squares method of measuring this difference suffers from three main drawbacks including local minima trapping, sensitivity to noise, and difficulties in reconstruction below reflecting layers. Unlike the local amplitude comparison in the least-squares method, the quadratic Wasserstein distance from the optimal transport theory considers both the amplitude differences and the phase mismatches when measuring data misfit. I will briefly review our earlier development and analysis of optimal transport-based inversion and include improvements, for example, a stronger convexity proof. The main focus will be on the third ``challenge'' with new results on sub-reflection recovery.10/29/2019 5:00:00 PM10/29/2019 6:00:00 PMFalse

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