Séminaire - Avril
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: avril.pdf.
- 10/04/2019 - Giovanni Forni (University of Maryland / Université Paris 7) - salle 01
Titre:
Effective weak mixing for translation flows and twisted cohomology
Resumé: We
study twisted ergodic integrals for translation flows on surfaces of
higher genus. The motivation is two-fold: on the one hand we want to
understand the deviation of ergodic averages for a simple example of
3-dimensional translation flow given by the product of a translation
flows on a higher genus surface and on a circle, on the other hand
there is a well-known connection between twisted ergodic integrals and
spectral measures of translation flows, already exploited in the work
of Bufetov and Solomyak, and speed of weak mixing, which gives an
effective version of a result with Avion weak mixing of translation
flows. The main new idea is a natural notion of twisted cohomology and
a cocycle dynamical system over the Teichmueller geodesic flows acting
on a twisted cohomology bundle. By introducing this cocycle we can then
apply methods of Hodge theory similar to those applied in the study of
the Kontsevich--Zorich cocycle. The talk will focus on these new
cohomological tools and the overall strategy of the argument.