Bruinier, Jan Hendrik Burgos Gil, José Ignacio Magnien, Jérémy

A Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties have a very rich geometric and arithmetic structure. For instance they are defined over a number field (the reflex field), they have ...

Bost, Jean-Benoît Magnien, Jérémy

In these lectures, I will firstly discuss diverse properties of the invariant h0θ and of its extensions to certain infinite dimensional generalizations of Euclidean lattices. Then I will present applications of this formalism to transcendence theory and to algebraization theorems in Diophantine geometry.

Forni, Giovanni Girard, Yohan

In these lectures we summarized results on the cohomological equation for translation flows on translation surfaces (myself, Marmi, Moussa and Yoccoz, Marmi and Yoccoz) and apply these results to the asymptotic of correlations for pseudo-Anosov maps, which were recently obtained by a direct method by Faure, Gouezel and Lanneau. In this vein, we con...

Matheus, Carlos Girard, Yohan

a) basic definitions and examples b) strata and genus c) reduced and primitive origamis, SL(2,R) action, Veech groups d) automorphisms and affine homeomorphisms e) homology of origamis f) Kontsevich-Zorich cocycle g) Lyapunov exponents of the Wollmilchsau

Ottaviani, Fiona Fargeon, Valérie Le Roy, Anne Offredi, Claudine

Une expérimentation impulsée par des chercheurs et des professionnels des politiques publiques visant à construire des indicateurs de bien-être soutenable territorialisée à l'échelle du territoire de l'agglomération grenobloise a émergé à la croisée des considérations scientifiques sur les indicateurs alternatifs (Sen et Stiglitz (2009), Perret (20...

Girard, Yohan Forni, Giovanni

In these lectures we summarized results on the cohomological equation for translation flows on translation surfaces (myself, Marmi, Moussa and Yoccoz, Marmi and Yoccoz) and apply these results to the asymptotic of correlations for pseudo-Anosov maps, which were recently obtained by a direct method by Faure, Gouezel and Lanneau. In this vein, we con...

Hervieu, Patrick Herrscher, Estelle

Peyre, Emmanuel Magnien, Jérémy

The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise these thin subsets. The slopes introduced by Jean-Benoît Bost are a useful tool for this problem. These ...

Wright, Alex Bastien, Fanny

We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no familiarity with earthquakes, and the first lecture will be devoted to preliminaries. The second lecture will cover the proof, and the final lecture ad...

Girard, Yohan Skripchenko, Sasha

1. Symbolic dynamics: Arnoux - Rauzy words and Rauzy gasket 2. Topology: Arnoux - Yoccoz example and its generalization 3. Novikov’s problem: how dynamics meets topology and together they help to physics 4. Lyapunov exponents for the Rauzy gasket: what do we know about them 5. Multidimensional fraction algorithms: why do they care 6. Open problem s...