Institut Fourier
L’Institut Fourier, laboratoire de mathématiques de Grenoble, est une
unité mixte de recherche CNRS/Université Grenoble Alpes. Ses activités
portent principalement sur les mathématiques fondamentales développées
autour de six grands thèmes de recherche : algèbre et géométries,
combinatoire et didactique, géométrie et topologie, physique
mathématique, probabilités, théorie des nombres. Ses recherches
s’ouvrent aussi à d’autres disciplines, telles que la biologie,
l’informatique et la physique. Depuis 2011, l’Institut Fourier filme ses
évènements scientifiques tels que : colloques, séminaires, écoles
d’été, conférences grand public, …
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Liste des programmes
The goal of this talk is to introduce a Gross--Zagier type formula,
which relates the arithmetic self-intersection number of the Hodge
bundle of a quaternionic Shimura curve over a totally real field to the
logarithmic derivative of the Dedekind zeta function of the base field
at 2. The proof is ...
Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given bythe Dynnikov coordinate system. In this talk we describe polynomial time algorithms for calculating the number of ...
In the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her count of Weil-Peterson volumes and her proof of Witten's conjecture, but only on the level of ...
In the first two lectures I will try to tell (or, rather, to give an idea) of how Maryam Mirzakhani has counted simple closed geodesics on hyperbolic surfaces. I plan to briefly mention her count of Weil-Peterson volumes and her proof of Witten's conjecture, but only on the level of ...
In the principal stratum in genus two, McMullen observed that something odd happens - there is only one nonarithmetic Teichmuller curve - the one generated by the decagon. This strange phenomenon begets another - a primitive translation surface in genus two admits a periodic point that is not a Weierstrass ...
The first part of the course will be devoted to some of the classicalresults about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification,abelianization, isomorphic rigidity, geometry of combinatorial models.In the second part we will explore some aspects of "big" mapping class groups, highlighting the ...
The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the second part we will explore some aspects of "big" mapping class ...
Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and group structure. Some of the periodic trajectories exhibit a surprising "dense but not equidistributed" behavior. I will show pictures of periodic ...
The mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those representations for locally varying families (Shiga). If time permit we will see how to apply this to prove ...
K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss: Basic definitions and examples- Geometry (algebraic, differential, etc.) of complex surfaces- Torelli theorems for K3 surfaces- Dynamics on K3s (Cantat, McMullen)- Analogies with flat surfaces- (time permitting) Integral-affine structures
