List of
Participants
Program
Travel
Information
Hotel
Organizers:
Riccardo
Biagioli
Frédéric Jouhet
Institut Camille
Jordan
Université
Claude Bernard Lyon 1
Contact:
slc (at) math.univlyon1.fr
SLC home page

80th Séminaire Lotharingien de Combinatoire
March
2528, 2018
Institut Camille
Jordan  Bâtiment Braconnier
Université Claude Bernard Lyon 1
43, Bd du 11 novembre 1918
69622 Villeurbanne  France
The
invited
speakers of this session are:
Boris Adamczewski (CNRS 
Université Claude Bernard Lyon 1, France)
Diagonals of rational functions
Abstract. A very rich interplay between combinatorics, arithmetic, and
geometry arises in the study of homogeneous linear differential
equations and especially of those that “come from geometry” and the
related study of Siegel Gfunctions. A remarkable result is that,
by adding variables, analytic solutions of many such differential
equations arise in a natural way from much more elementary functions:
multivariate rational functions.
The underlying process is called diagonalization. More generally, it
allows one to associate with any multivariate power series with
coefficients in any ring a onevariable power series (by collecting
only the coefficients on its diagonal). Applying this operation to
multivariate rational power series leads to the class of diagonals of
rational functions, or just diagonals for short.
The aim of these lectures is to provide an introduction to diagonals.
After describing their main properties, I will discuss some
arithmetical problems involving their reduction mod p and their link
with automata theory.
Stéphane Gaussent (Université Jean Monnet SaintÉtienne,
France)
On
some IwahoriHecke algebras associated to KacMoody groups
Abstract. In the first introductory lecture, we will recall some
defintions of various IwahoriHecke algebras. Then, we will end the
talk with the computation of the structure constants of the spherical
Hecke algebras in terms of Hecke paths. In the second talk, we will
explain how to generalise some algebras defined earlier to the context
of KacMoody root systems. In the last talk, we will explain how to
prove a Macdonald's formula in the KacMoody setting. The formula we
talk about here is the one giving the image of the Satake isomorphism
between the spherical Hecke algebra and the algebra of (generalize)
symmetric functions.
