Séminaire - Mars
Le séminaire aura lieu un mercredi par mois de 14h à 15h à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: mars.pdf.
- 13/03/2019 - Michael Magee (Durham University) - salle 421
Titre:
Selberg's Eigenvalue Conjecture for Moduli Spaces of Abelian
Differentials
Resumé: I'll begin by discussing Selberg's eigenvalue conjecture,
that predicts a uniform spectral gap for the Laplacian
on a special family of arithmetic Riemann surfaces.
Selberg's conjecture can be restated in terms of the Teichmuller dynamics
of abelian differentials on a torus. Based on this, Yoccoz made
a generalization of Selberg's conjecture for connected components
of strata of abelian differentials on higher genus surfaces.
I will explain how I have proved an approximation to Selberg's conjecture
in higher genus, and highlight some of the interesting ingredients involved,
including the recent resolution of a conjecture of Zorich by Avila-Matheus-Yoccoz
and Gutierrez-Romo. If I have time, I'll explain how this all fits into a broader program
of automorphic forms on moduli spaces.