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Archive : Inverse Problems and Analysis

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Dominique Guillot, University of DelawareDominique Guillot, University of DelawareEWG 336Title:Totally nonnegative GCD matrices and kernels ‌ <br><br>‌ ‌ Abstract:‌Abstract: Let X=(x_1, ... ,x_n) be a vector of distinct positive integers. The n x n matrix with ij-th entry equal to gcd(x_i,x_j), the greatest common divisor of x_i and x_j, is called the GCD matrix on X. By a surprising result of Beslin and Ligh (1989), all GCD matrices are positive definite. In this talk, we will discuss new characterizations of the GCD matrices satisfying the stronger property of being totally nonnegative (i.e., all their minors are nonnegative). <br>‌ ‌ Joint work with Lucas Wu. 2/25/2020 6:30:00 PM2/25/2020 7:30:00 PMFalse
Dr. Apoorva Khare, Indian Institute of Science Dr. Apoorva Khare, Indian Institute of Science PRN238Title: Polymath 14: Groups with norms <br><br> Abstract: Consider the following three properties of a general group G: <br> (1) Algebra: G is abelian and torsion-free. <br> (2) Analysis: G is a metric space that admits a "norm", namely, a translation-invariant metric d(.,.) satisfying: d(1,g^n) = |n| d(1,g) for all g in G and integers n. <br> (3) Geometry: G admits a length function with "saturated" subadditivity for equal arguments: l(g^2) = 2 l(g) for all g in G. <br> While these properties may a priori seem different, in fact they turn out to be equivalent. The nontrivial implication amounts to saying that there does not exist a non-abelian group with a "norm". <br> We will discuss motivations from analysis, probability, and geometry; then the proof of the above equivalences; and finally, the logistics of how the problem was solved, via a PolyMath project that began on a blogpost of Terence Tao. <br> (Joint - as D.H.J. PolyMath - with Tobias Fritz, Siddhartha Gadgil, Pace Nielsen, Lior Silberman, and Terence Tao.)1/29/2020 7:30:00 PM1/29/2020 8:30:00 PMFalse
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

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