Nalini Anantharaman (Strasbourg)
22-26 août 2016

Diaporama de la conférence

CHAIRE AISENSTADT CHAIR 2016

Série de conférences / Series of lectures

Semestre thématique : Méthodes probabilistes en géométrie, topologie et théorie spectrale

CRM Thematic Semester: Probabilistic Methods in Geometry, Topology and Spectral Theory

Nalini Anantharaman (Université de Strasbourgh)

Conférence s'adressant à un large auditoire scientifique
Lecture suitable for a general scientific audience

LIEU/LOCATION: Centre de recherches mathématiques
Pavillon Roger-Gaudry, Université de Montréal
Salle / Room M-415

DATE : Lundi 22 août / Monday, August 22 16h00 / 4:00 pm

Vidéo de la conférence / Video of the lecture

Quantum ergodicity on Riemannian manifolds

Quantum ergodicity" in the traditional sense deals with the question of (de)localization of eigenfunctions of the laplacian on a Riemannian manifold, in the limit of high eigenvalues. In this "semiclassical limit", it is known that the behavior of eigenfunctions bears some relation with the ergodic properties of a dynamical system called the "geodesic flow".

Une réception suivra la conférence au salon Maurice L'Abbé, Pavillon André-Aisenstadt (salle 6245).

A reception will follow the lecture at the Salon Maurice-L'Abbé, Pavillon André-Aisenstadt (room 6245).

DATE: Mardi 23 août / Tuesday, August 23

LIEU/LOCATION : Centre de recherches mathématiques
Pavillon Roger-Gaudry, Université de Montréal
Salle / Room M-415

16:00 / 4:00 pm

Vidéo de la conférence / Video of the lecture

Quantum ergodicity on large graphs I: Regular graphs

In this talk, we consider finite regular graphs whose size grows to infinity, and discuss some delocalization results for eigenfunctions of the adjacency matrix (joint w. Le Masson). We will also discuss connections between QE on graphs and QE on manifolds, mostly through the work of Lindentrauss and collaborators on "arithmetic" quantum ergodicity.

DATE: Mercredi 24 août / Wednesday, August 24

LIEU/LOCATION :Centre de recherches mathématiques
Pavillon Roger-Gaudry, Universite de Montreal
Salle / Room M-415

16:00 / 4:00 pm

Vidéo de la conférence / Video of the lecture

Quantum ergodicity on graphs II : Perspectives on other models

Results on QE on discrete graphs are so far restricted to regular graphs (for which all points have the same number of neighbours). Here we will discuss possibilities of extension to other models : Anderson model on regular graphs (work in progress with Mostafa Sabri), percolation graphs on regular graphs. We will also put our results into perspective by comparing them to recent results on eigenvectors of random matrices.