Peralta-Salas' seminar reminder

[Antonio Lerario]

Dear All,

this is a reminder for today's seminar.
Please note that, given the current situation, this seminar will be
accessible only from remote.

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
Zoom link:
https://sissa-it.zoom.us/j/83546552136?pwd=QWk4ZHhHYm0wbVg0WWdKTSsweEJydz09
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.


More information on the seminars in this series can be found here:
https://sites.google.com/view/geometric-structures/.
Everyone is welcome!

Best,
Antonio


-- 
*http://people.sissa.it/~lerario <http://people.sissa.it/~lerario>*