Séminaire - Mai
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: mai.pdf.
- 21/05/2025 - Viveka Erlandsson (University of Bristol)
salle Olga Ladyjenskaïa (ex-salle 01)
Titre: Determining
the shape of a billiard table from its bounces
Resumé: Consider
a billiard table shaped as a Euclidean polygon with labeled sides
(where the angles are allowed to be irrational multiples of \(\pi\)). A
ball moving around on the table determines a bi-infinite
“bounce sequence” by recording the labels of the
sides it bounces off, and the set of all possible bounce sequences
gives the bounce spectrum of the table. In this talk I will explain why
the bounce spectrum essentially determines the shape of the table: with
the exception of a very small family (right-angled tables), if two
tables have the same bounce spectrum then they have to be related by a
Euclidean similarity. In the language of Euclidean cone surfaces, this
can be phrased as another rigidity statement: the metric is
(generically) determined by the endpoints of its non-singular geodesics
in its universal cover. Time allowing, I will discuss some ongoing work
generalizing these results to billiards with obstacles. This is joint
work with Moon Duchin, Chris Leininger, and Chandrika Sadanand.
- 21/05/2025 - Thomas Le Fils (The University of Sydney)
salle Olga Ladyjenskaïa (ex-salle 01)
Titre: Periods of
abelian differentials
Resumé: Integrating
an abelian differential along paths joining its zeroes
defines a
representation of its relative homology into \(\mathbb{C}\): its
periods,
which provide local charts on each stratum.
This naturally leads to several questions:
- Which representations arise in this way?
- Can the periods of an abelian differential help determine the
connected component of the stratum to which it belongs?
The aim of this talk will be to answer these questions, refining a
theorem of Haupt from 1920.