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Archive : Inverse Problems and Analysis

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Fritz Gesztesy, Baylor UniversityFritz Gesztesy, Baylor UniversityZoomTitle: The limiting absorption principle and continuity properties of the spectral shift function for massless Dirac-type operators <br> Abstract: We report on recent results regarding the limiting absorption principle for multi-dimensional, massless Dirac-type operators and continuity properties of the associated spectral shift function. <br> This is based on various joint work with A. Carey, J. Kaad, G. Levitina, R. Nichols, D. Potapov, F. Sukochev, and D. Zanin. 11/6/2020 6:30:00 PM11/6/2020 7:30:00 PMFalse
Prof. Ben Hayes, University of VirginiaProf. Ben Hayes, University of VirginiaZoom<br>Title: A random matrix approach to the Peterson-Thom conjecture <br> <br>Abstract: The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in a unique maximal amenable subalgebra. This conjecture is motivated by related results in Popa's deformation/rigidity theory and Peterson-Thom's results on L^{2}-Betti numbers. We present an approach to this conjecture in terms of so-called strong convergence of random matrices by formulating a conjecture which is a natural generalization of the Haagerup-Thorbjornsen theorem whose validity would imply the Peterson-Thom conjecture. This random matrix conjecture is related to recent work of Collins-Guionnet-Parraud. <br>10/30/2020 5:30:00 PM10/30/2020 6:30:00 PMFalse
Kelly Bickel, Bucknell University Kelly Bickel, Bucknell University Zoom Title: Matrix Monotonicity in the Quasi-Rational Setting <br> Abstract: In this talk, we will show quasi-rational functions on the bidisk D^2 (intuitively, inner functions that are rational in one of the variables) yield functions that preserve matrix inequalities on rectangles in R^2. This result provides a partial answer to a 2012 conjecture posed by Agler, McCarthy, and Young about local-to-global matrix monotonicity of two-variable functions and is joint work with J.E. Pascoe and Ryan Tully-Doyle. <br>10/23/2020 5:30:00 PM10/23/2020 6:30:00 PMFalse
Prof. Murali Vemuri, Indian Institute of Technology (BHU)Prof. Murali Vemuri, Indian Institute of Technology (BHU)ZoomTitle: INDUCTIVE ALGEBRAS <br> Abstract: Let R be an irreducible unitary representation of a group G on a Hilbert space H. An R-inductive algebra is a weakly closed abelian algebra of bounded operators on H which is normalised by R(G). The identification of inductive algebras may shed light on the possible realizations of H as a space of sections of a homogeneous vector bundle. This talk will be a brief introduction to the subject. 10/16/2020 5:30:00 PM10/16/2020 6:30:00 PMFalse

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