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UBC cIRcle BIRS Workshop Lecture Videos Logo
Local universality for zeros and critical points of monochromatic random waves
Banff International Research Station for Mathematical Innovation and Discovery
Canzani, Yaiza — 2019-03-13 In this talk we will discuss the asymptotic behavior of zeros and critical points for monochromatic random waves on compact, smooth, Riemannian manifolds, as the energy of the waves grow to infinity. This is joint work with Boris Hanin Non UBC Unreviewed Author affiliation: University of North Carolina at Chapel Hill Faculty http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
On the growth of eigenfunctions averages
Banff International Research Station for Mathematical Innovation and Discovery
Canzani, Yaiza — 2019-03-20 In this talk we discuss the behavior of Laplace eigenfunctions when restricted to a fixed submanifold by studying the averages given by the integral of the eigenfunctions over the submanifold. In particular, we show that the averages decay to zero when working on a surface with Anosov geodesic flow regardless of the submanifold (curve) that one picks. This is based on joint works with John Toth and Jeffrey Galkowski. Non UBC Unreviewed Author affiliation: University of North Carolina at Chapel Hill Faculty http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Structure of the zero sets of random waves on a manifold
Banff International Research Station for Mathematical Innovation and Discovery
Canzani, Yaiza — 2016-11-30 There are several questions about the zero set of Laplace eigenfunctions that have proved to be extremely hard to deal with and remain unsolved. Among these are the study of the size of the zero set, the study of the number of connected components, and the study of the topology of such components. A natural approach is to randomize the problem and ask the same questions for the zero sets of random linear combinations of eigenfunctions. In this talk I will present some recent results in this direction. Non UBC Unreviewed Author affiliation: Harvard University Postdoctoral http://creativecommons.org/licenses/by-nc-nd/4.0/
UBC cIRcle BIRS Workshop Lecture Videos Logo
Eigenfunction concentration via geodesic beams
Banff International Research Station for Mathematical Innovation and Discovery
Canzani, Yaiza — 2023-10-26 A vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles, is dictated by the behavior of Laplace eigenfunctions. Because of this, it is crucial to understand how various measures of eigenfunction concentration respond to the background dynamics of the geodesic flow. In collaboration with J. Galkowski, we developed a framework to approach this problem that hinges on decomposing eigenfunctions into geodesic beams. In this talk, I will present these techniques and explain how to use them to obtain quantitative improvements on the standard estimates for the eigenfunction's pointwise behavior, Lp norms, and Weyl Laws. One consequence of this method is a quantitatively improved Weyl Law for the eigenvalue counting function on all product manifolds. Non UBC Unreviewed Author affiliation: University of North Carolina at Chapel Hill Faculty
UBC cIRcle BIRS Workshop Lecture Videos Logo
On the behavior of random linear combinations of Laplace eigenfunctions​
Banff International Research Station for Mathematical Innovation and Discovery
Canzani, Yaiza — 2017-06-13 There are several questions about the behavior of Laplace eigenfunctions that have proved to be extremely hard to deal with and remain unsolved. Among these are the study of their number of critical points, the study of the size of their zero set, the study of the number of connected components of their zero set, and the study of the topology of such components. A natural approach is to randomize the problem and ask the same questions for the zero sets of random linear combinations of eigenfunctions. In this talk I will present several results in this direction. This talk is based on joint works with Boris Hanin and Peter Sarnak. Non UBC Unreviewed Author affiliation: University of North Carolina, Chapel Hill Postdoctoral http://creativecommons.org/licenses/by-nc-nd/4.0/

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