Geometric Structures: Daniel Peralta-Salas' seminar

Antonio Lerario lerario at
Fri Oct 23 17:33:36 CEST 2020

Dear All,

this is to announce the first seminar from the series "Geometric Structures

Speaker: Daniel Peralta-Salas (ICMAT)
Title: The topology of the nodal sets of eigenfunctions and a problem of
Michael Berry.

Venue: Tuesday, October 27, 4pm-5pm, room A-005 (maximum 25 people inside)
and on zoom

Zoom link:
Meeting ID: 835 4655 2136
Passcode: geometry

Abstract: In 2001, Sir Michael Berry conjectured that given any knot there
should exist a (complex-valued) eigenfunction of the harmonic oscillator
(or the hydrogen atom) whose nodal set contains a component of such a knot
type. This is a particular instance of the following problem: how is the
topology of the nodal sets of eigenfunctions of Schrodinger operators? In
this talk I will focus on the flexibility aspects of the problem: either
you construct a suitable Riemannian metric adapted to the submanifold you
want to realize, or you consider operators with a large group of symmetries
(e.g., the Laplacian on the round sphere, or the harmonic quantum
oscillator), and exploit the large multiplicity of the high eigenvalues. In
particular, I will show how to prove Berry's conjecture using an inverse
localization property. This talk is based on different joint works with A.
Enciso, D. Hartley and F. Torres de Lizaur.

This series of seminars focuses on Real Geometry, touching topics from real
algebraic geometry, control theory, convex geometry, nodal sets, random
topology and subriemannian geometry. More information can be found here:
Everyone is welcome!


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