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Dalhousie-AARMS AAMP Seminar: Milivoje Lukic (Rice U.)
March 17, 2023 @ 4:00 pm - 5:00 pm
Title: Universality limits for orthogonal polynomialsAbstract: It is often expected that the local statistical behavior ofeigenvalues of some system depends only on its local properties; forinstance, the local distribution of zeros of orthogonal polynomials shoulddepend only on the local properties of the measure of orthogonality. Thisphenomenon is studied using an object called the Christoffel-Darbouxkernel. The most commonly studied case is known as bulk universality,where the rescaled limit of Christoffel-Darboux kernels converges to thesine kernel.In this talk, we will survey this subject, prior results, and a recentresult which gives for the first time a completely local sufficientcondition for bulk universality. The new approach is based on a matrixversion of the Christoffel-Darboux kernel and the de Branges theory ofcanonical systems, and it applies to other self-adjoint systems with 2×2transfer matrices such as continuum Schrodinger and Dirac operators.The talk is based on joint work with Benjamin Eichinger (TechnicalUniversity Wien) and Brian Simanek (Baylor University).
The Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over either Zoom and/or in Chase 227 depending on the speaker. If you would like to attend, please email the organizers for connection details.