Séminaire - Octobre
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: octobre.pdf.
- 12/10/2022 - Yilin Wang (IHES) - salle 314
Titre: From SLE
to Weil-Petersson Universal Teichmuller space
Resumé:
The universality of Brownian motion underlies the appearance of SLE in
conformally invariant 2D systems. The action functional of Brownian
motion, namely the Dirichlet energy, corresponds to the Loewner energy
for a Jordan curve. This energy, intuitively speaking, measures the
roundness of a Jordan curve and the density of SLE around the curve.
Furthermore, this energy is shown by Takhtajan and Teo to be a Kahler
potential on the space of Weil-Petersson quasicircles, identified with
the Weil-Petersson universal Teichmuller space. I will overview
different geometric and probabilistic descriptions of the Loewner
energy and Weil-Petersson Teichmuller space and discuss further
development by exploring those links.