Séminaire - Novembre
Le séminaire aura lieu un mercredi du mois (exceptionnellement deux exposés) de 14h à 15h et 15h30 à 16h30 à l'Institut Henri Poincaré à Paris. Pour télécharger l'affiche du mois: novembre.pdf.
- 27/11/2024 - James Farre (Max Planck Institute)
salle Olga Ladyjenskaïa (ex-salle 01)
Titre: Affine laminations
and coaffine representations
Resumé: A
surface subgroup \(\Gamma\) of \(PSL(4,\mathbb{R})\) is convex
cocompact if it preserves a nice convex set in projective 3-space on
which it acts with compact quotient. In this talk, we study surface
group actions on coaffine 3-space — a subgeometry of projective
geometry. After an introduction to coaffine geometry, I will describe
the structure of the boundary of the convex core associated to a convex
cocompact surface group action on coaffine space: it is a 2-dimensional
convex projective structure bent along a geodesic lamination according
to an affine measure whose holonomy depends on the dynamics of a
certain linear cocycle over the geodesic flow of the surface. This is
joint work with Martin Bobb.
- 27/11/2024 - Jayadev Athreya (University of Washington)
salle Olga Ladyjenskaïa (ex-salle 01)
Titre: Billiards
in Rational Prisms
Resumé: We
survey what we know about the dynamics of billiards in rational prisms,
that is, right prisms over rational polygons. We will discuss how to
use beautiful ideas of Furstenberg and Veech to make connections
between mixing properties of billiards in polygons to ergodic
properties of billiards in prisms, and to produce explicit non-ergodic
examples for billiards in prisms over certain regular polygons. We
crucially use a construction of Mercat's for constructing
eigenfunctions for substitutions, and give a geometric explanation of
his construction. There will be lots of examples, and lots of pictures.
This is joint work with Nicolas Bedaride, Pat Hooper, and Pascal Hubert.