ON-LINE: Number Theory Seminar

See below for more organisational information.

Speaker: Jasmin Matz (KU)

Title: Quantum ergodicity in the level aspect

Abstract: For a compact Riemannian manifold $M$ and an orthonormal basis $B$ of $L^2(M)$ consisting of Laplace eigenfunctions, the property of $M$ satisfying quantum ergodicity asserts that there is a sequence of density $1$ of functions $f$ in $B$ with Laplace eigenvalue going to infinity such that the measures $\lvert f \rvert^2 \, d_M x$  weak$*$-converges to the Riemannian measure $d_M x$ on $M$.
Due to work by Shnirelman and others this is known to hold for $M$ with ergodic geodesic flow.

We want to change perspective now, considering not one fixed manifold and Laplace eigenfunctions in the high energy limit, but a sequence of Benjamini-Schramm convergent Riemannian manifolds $M_j$ together with
Laplace eigenfunctions $f$ whose eigenvalues vary in short intervals.
This perspective has been recently studied in the context of graphs by Anantharaman and Le Masson, and for hyperbolic surfaces and manifolds by Abert, Bergeron, Le Masson, and Sahlsten.
In my talk I want to discuss joint ongoing work with F. Brumley in which we study a higher rank case, namely sequences of compact quotients of $\operatorname{SL}(n,R) / \operatorname{SO}(n)$.

Organisational information

Event: This is part of a series of number theory seminars which will take place online, due to the current exceptional situation. Each of the new events will be organised as a Zoom meeting. Apart from the speaker, there will be a designated "host" of the event, whose job will be to moderate access, to collect the questions (that can be asked in the Zoom chat) and so on.

Participation: If you want to participate but you haven't taken part in a previous edition of this seminar and you are not a member of the Algebra and Number Theory group of the University of Copenhagen, please send an email to the host. You will be added to the mailing list for this virtual seminar. Everyone in the mailing list will receive an email with the link to join the Zoom meeting one hour before the starting time of the talk.

Host: Riccardo Pengo (KU). Email: pengo@math.ku.dk.

Date and time: 15/05/2020, from 15.30 to 16.30 (Copenhagen time).

Place: Zoom meeting