ALGANT Graduation Days 2016

18 juil. 2016, 08:00 → 21 juil. 2016, 23:59 Europe/Paris

Université de Bordeaux

July 18-21, 2016: The University of Bordeaux will host the ALGANT graduation ceremony of the 2014-2016 intake on Wednesday, 20^th July. 

Students will defend their Master thesis on Monday, and Tuesday, 18 - 19^th July,.

On this occasion, we will also celebrate the 10th graduation of the ALGANT Master.

ALGANT students, past and present, Thursday, 21^st July will be your day, a unique occasion to meet together. There will be discussions, scientific talks, and entertainment.

Mark your calendars!

  ALGANT graduation ceremony 2015

 

Contact: Deborah Didio   deborah.didio@u-bordeaux.fr

 

 

lundi 18 juillet

Arrival of participants

Consortium meeting

Lunch break

2014-2016 ALGANT ERASMUS MUNDUS Students dissertation defense: Part 1

Dinner

mardi 19 juillet

2014-2016 ALGANT ERASMUS MUNDUS Students dissertation defense: Part 2

Lunch break

2014-2016 ALGANT ERASMUS MUNDUS Students dissertation defense: Part 3

Dinner

mercredi 20 juillet

Arrival of participants

Official speeches

Joint Degree Award ceremony

Lunch

Cultural/Social activity

Dinner

jeudi 21 juillet

Arrival of participants: Morning coffee

Introduction to the day

Jean-Pierre SERRE: Frobenius distributions and hyperelliptic curves

Coffee/tea break

Mauro Porta: Derived analytic geometry

I will survey the main motivations and applications of my phd thesis. I will especially focus on the non-archimedean side and sketch some steps of a program of Kontsevich and Soibelman that require the use of derived non-archimedean geometry.

Sara Checcoli: The explicit Mordell Conjecture for families of curves

The Mordell Conjecture, proved by Faltings, states that a curve of genus at least 2 over a number field k has only finitely many k-rational points.
Unfortunately, the proof of this conjecture is neither explicit nor effective, in the sense that it does not provide a bound on the 'size' of the points, nor a method to find such a bound. Effective methods in this context are rare and often difficult to apply to obtain explicit results.

In this talk I will present a joint work with F. Veneziano and E. Viada in which we prove, in particular, the explicit Mordell Conjecture for curves in $E^N$, where $E$ is an elliptic curve without CM having Mordell-Weil group of rank 1. For certain families of curves in $E\times E$, of quite general shape and increasing genus, we give a method of easy application to bound the height of their rational points. In many examples (more than 10^4) the bounds we obtain are so small that a computer search for the rational points is faisable. This last is made with PARI-GP using an algorithm by K. Belabas.

Lunch

Arno Kret: The Newton stratification of Shimura varieties

Frans Oort examined various stratifications of the moduli space of principally
polarized abelian varieties in characteristic p. It is conjectured that Newton strata exist on all Shimura varieties. In this talk I will explain various open questions regarding the Newton stratification.

Olga Balkanova: Moments of L-functions and applications

Problems of different nature can be phrased in terms of central L-values. Therefore, asymptotic evaluation of moments of L-functions near the critical line is an important subject in analytic number theory. In this talk we prove asymptotic formulas for the mean values of L-functions associated to the family of primitive forms and discuss several applications of these results.

Stefano Morra: Serre weights and Breuil's lattice conjectures in dimension three

Let F/Q be a number field where p is unramified and r : Gal(F /F ) → GL_3(Q_p ) a
continuous Galois representation. We assume that r is automorphic for U(3) and the
p-adic local parameters of r at p are tamely potentially crystalline, with Hodge-Tate
weights (0,1,2).
The local/global compatibility conjecture in the p-adic local Langlands correspon-
dence predicts that the r-eigenspace in the integral ́etale cohomology on the adelic
points of U(3) with infinite level at p, should only depend on the p-adic local para-
meter associated to r, in some explicit way.
In this talk we prove the local/global compatibility conjecture when considering a
tame level at p, under mild technical hypotheses on the mod p-reduction of r. More
precisely, we show that the integral structure cut out by the global ́etale cohomology
on the tame ́etale local system giving rise to r depends only on the p-adic local
parameter.
The proof relies on the explicit construction of local Galois deformation rings in
dimension three, the description of their special fiber in automorphic terms via the
Breuil-M ́ezard conjecture, a new technique (which is a mixture of both global and
local methods) to compute the mod p reduction of Z_p -lattices in tame K-types.
This is a joint work with Dan Le, Viet-Bao Le Hung and Brandon Levin.

Coffee/tea break

Round Table

Aglaya Myropolska: Geometry and Probability on Groups

The Banach-Tarski paradox led von Neumann in 1929 to the definition of amenability for groups - this phenomenon later was reformulated and found applications in various subjects in mathematics such as geometric group theory, functional analysis, probability, operator algebras etc. In this talk we will discuss amenability from a group theorist' point of view with a glance on its geometric and probabilistic properties.

Andrii Dmytryshyn: Coupled Sylvester-type matrix equations and block diagonalization

We prove Roth-type theorems for systems of matrix equations including an arbitrary mix of Sylvester and ⋆-Sylvester equations,

in which the transpose or conjugate transpose of the unknown matrices also appear. In full generality, we derive consistency conditions by proving that such a system has a solution if and only if the associated set of 2x2 block matrix representations of the equations are block diagonalizable by (linked) equivalence transformations. Various applications leading to several particular cases have already been investigated in the literature, some recently and some long ago. Solvability of these cases follow immediately from our general consistency theory.

We also show how to apply our main result to systems of Stein-type matrix equations.

Launch of ALGANT Alumni committee and final speech

18:30 Food time