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Archive : Inverse Problems and Analysis

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Prof. Fiora Cakoni Prof. Fiora Cakoni ZoomTitle: Transmission Eigenvalues for a Scattering Problem in Hyperbolic Geometry <br><br> Abstract: We will discuss the concept of transmission eigenvalues in scattering theory for automorphic forms on fundamental domains generated by discrete groups acting on the hyperbolic upper half complex plane. In particular, we consider Fuchsian groups of type I. In a given scattering media, transmission eigenvalues are related to wave numbers for which one can send an incident wave that doesn't scatterer. The notion of transmission eigenvalues, or non-scattering energies, is well studied in the Euclidean geometry, where in some cases these eigenvalues appear as zeros of the scattering matrix. As opposed to scattering poles, in hyperbolic geometry such a connection between zeros of the scattering matrix and non-scattering energies is not studied. Our study does just this for particular arithmetic groups. For such groups, using existing deep results from analytic number theory, we reveal that the zeros of the scattering matrix, consequently non-scattering energies, are directly expressed in terms of the zeros of the Riemann zeta function. We provide Weyl’s asymptotic laws for the transmission eigenvalues in those cases along with estimates on their location in the complex plane. Finally, we will discuss a few open problems. This talk is based on a joint paper with Sagun Chanillo.9/25/2020 5:30:00 PM9/25/2020 6:30:00 PMFalse
Prof. David Kerr, Texas A&M UniversityProf. David Kerr, Texas A&M UniversityZoomTitle: C*-simple groups with property Gamma <br><br> Abstract: I will explain how one can use the theories of topological full groups and dynamical entropy to construct large classes of simple finitely generated groups which are C*-simple and have property Gamma. This is joint work with Robin Tucker-Drob. 9/18/2020 5:30:00 PM9/18/2020 6:30:00 PMFalse
Prof. Ivan Todorov, University of DelawareProf. Ivan Todorov, University of DelawareZoomTitle: Non-local games: operator algebraic approaches <br><br> Abstract: The study of non-local games has involved fruitful interactions between operator algebra theory and quantum physics, with a starting point the link between the Connes Embedding Problem and the Tsirelson Problem, uncovered by Junge et al (2011) and Ozawa (2013). Particular instances of non-local games, such as binary constraint system games and synchronous games, have played an important role in the pursuit of the resolution of these problems. In this talk, I will summarise part of the operator algebraic toolkit that has proved useful in the study of non-local games and of their perfect strategies, highlighting the role C*-algebras and operator systems play in their mathematical understanding. 9/11/2020 5:30:00 PM9/11/2020 6:30:00 PMFalse
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

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