9h3010h30: Yûzuke Okuyama
(Kyoto Institute of Technology)
A Mahlertype
estimate of weighted Fekete sums
on the Berkovich projective line
We will
talk about a Mahlertype estimate of weighted Fekete sums on the Berkovich projective line, which is asymptotically
sharp.
10h4511h45: Marie Albenque
(CNRS  Ecole Polytechnique)
Convergence
de cartes planaires aléatoires
In
the last years, numerous families of planar maps (embeddings of planar
graphs in the sphere) have been shown to converge to the Brownian map
introduced by Miermont and Le Gall. I’ll describe in this talk this
result of Miermont and Le Gall together with its context and will prove
a similar result for simple triangulations.
This work relies first on a bijection between simple triangulations and
a certain class of decorated trees. Then the distance in the maps can
be studied with the help of some canonical « leftmost paths », which
behave well both in the map and in the tree. I’ll emphasize the
combinatorial constructions that play a major role in this work and
which gives a glimpse of into the structure of the Brownian map.
11h4513h45:
Déjeuner
13h4514h45: Frédéric Bayart (Université Blaise Pascal)
Central
limit theorems in linear dynamics
Given a
bounded operator T on a
Banach space X, we study the
existence of a probability measure µ
on X such that, for many
functions f : X>K, the sequence (f + ... + f o T^{n1})/n^{1/2}
converges in distribution to a Gaussian random variable.
15h16h: Mariusz Lemanczyk (Nicolaus
Copernicus University)
Approximate
orthogonality of powers for Rokhlin extensions of rotations
An
automorphism T is called to
have asymptotically orthogonal powers (AOP),
if its different prime powers T^p and T^q become closer and closer to be disjoint in the sense of
Furstenberg when p,q tend to infty. Quasidiscrete
spectrum automorphisms are known to enjoy the
AOP property. I will show how this property can be achieved in the
class of socalled Rokhlin extensions of
irrational rotations. This will allow us to
produce ergodic sequences (a_n)
of integers along which, for any uniquely
ergodic homemorphism S, we have all observables f(S^{a_n}x), (n in N), orthogonal
to any multiplicative arithmetic function u from N to C,
with u at most 1. The talk is based on my joint work with Joanna
KulagaPrzymus.
