Recently, hyperbolic versions of uniform planar maps have attracted a great deal of attention. These maps are conjectured to be local limits of uniform maps embedded on high genus surfaces. First, I will describe a resolution of this conjecture for unicellular (or one-face) maps. Although for other cases this still remains a conjecture, several possible candidates have been constructed. I will give a brief overview of these models, their construction and geometric properties. I will also discuss behaviour of random walks (e.g. their speed) on them and how the ''final behaviour" of random walks on them can be nicely described via their circle packings. Parts of these works are joint with Omer Angel, Guillaume Chapuy, Nicolas Curien, Tom Hutchcroft and Asaf Nachmias.

(ATTENTION jour inhabituel)
Given a curve over a dvr of mixed characteristic 0-p with smooth generic fiber and with semistable reduction, I will present a criterion for good reduction in terms of the (unipotent) p-adic étale fundamental group of its generic fiber.

Page web du séminaire

The central axis of the famous DNA double helix is often constrained or even circular.   The topology of this axis can influence which proteins interact with the underlying DNA. Subsequently, in all cells there are proteins whose primary function (type II topoisomerases)  is to change the DNA axis topology — for example converting a torus link into an unknot. Additionally, there are several protein families (most importantly, site-specific recombinases) that change the axis topology as a by-product of their interaction with DNA.

This talk will describe some typical DNA conformations, and the families of proteins that change these conformations. I'll present a few examples illustrating how 3-manifold topology (including Dehn surgery and Heegaard Floer homology) have been useful in understanding certain DNA-protein interactions, and discuss the most common techniques used to attack these problems.

(horaire d’hiver)

In this talk, we will introduce the theory of (φ,Γ)-modules for general adic spaces. This is a joint work with Kedlaya.

Page web du séminaire

Une des définitions possibles des nombres de Hurwitz est qu'ils comptent certaines cartes étiquetées. De même que les cartes planaires sont en bijection avec des arbres plans (ou ordonnés), ces cartes étiquetées sont en bijection avec des arbres étiquetés de type Cayley. Le but de l'exposé sera de montrer comment l'étude de ces arbres permet de d'obtenir de nouvelles formules pour les nombres de Hurwitz doubles ainsi que des propriétés de polynomialité.

Considérons une marche aléatoire simple sur un arbre de Galton-Watson critique conditionné à avoir une hauteur supérieure à $n$. La loi du point d'atteinte de la hauteur $n$ par la marche aléatoire s'appelle la mesure harmonique au niveau $n$. Il est bien connu que le cardinal de l'ensemble des sommets de l'arbre au niveau $n$ est de l'ordre de $n$. En 2013 Curien et Le Gall ont prouvé qu'il existe une constante $beta=0.78…$ telle que la mesure harmonique est portée, à un ensemble de masse arbitrairement petite près, par un ensemble de cardinal de l'ordre de $n^beta$. Dans cet exposé, nous présentons l'existence d'une nouvelle constante universelle $lambda=1.21…$ telle que, avec grande probabilité, la mesure harmonique portée par un sommet typique à la hauteur $n$ est de l'ordre $n^{-lambda}$.

Séminaire Laurent Schwartz — EDP et applications

Much of black hole thermodynamics is limited to systems with a high degree of symmetry. In this talk, I will discuss a non-stationary, non-axisymmetric black hole spacetime that nevertheless admits a standard thermodynamics: a black hole corotating with an orbiting moon. More precisely, we consider a Kerr black hole perturbed by a particle on the circular orbit whose frequency matches that of the event horizon. The key point is that the spacetime has a helical Killing vector that generates the event horizon, allowing the surface gravity to be defined in the standard way. The surface gravity is uniform on the horizon and should correspond to the Hawking temperature of the black hole. We calculate the change in surface gravity/temperature, finding it negative: the moon has a cooling effect on the black hole. We also calculate the area/entropy of the perturbed black hole, finding no change from the background Kerr value.

I will present an overview of the work that has gone into formulating a theory of tidal deformations and dynamics of black holes in general relativity. This includes a description of the tidal environment around a black hole, a description of the tidal deformation in terms of the intrinsic geometry of the event horizon, and a description of how the black hole can exchange energy and angular momentum with its tidal environment.