Differential Galois theory in Strasbourg

Liste des contributions

1. Notions of difference closures of difference fields.

Mlle Zoé Chatzidakis

04/09/2019 14:00

It is well known that a differential field K of characteristic 0 is contained in a differential field which is differentially closed and has the property that it K-embeds in every differentially closed field containing K. Such a field is called a differential closure of K, and it is unique up to K-isomorphism. The difference closure is what model-theorists call a "prime model".

One can ask...

9. Inverse problem for germs of parabolic diffeomorphisms of the complex line

Loïc Teyssier

04/09/2019 15:30

5. Quotients and equations

Martin Martin-Pizarro

05/09/2019 09:30

Quotients are ubiquitous in Mathematics, and a general question is whether a certain category of sets allows quotients. For the category of definable sets in a given structure, the model theoretic approach is called elimination of imaginaries. For algebraically closed fields, Chevalley’s theorem and the existence of a field of definition of a variety imply that a quotient of a Zariski...

7. The Riemann-Hilbert mapping in genus two

Viktoria Heu

05/09/2019 11:00

6. On Miyake's algorithm for formal reduction of linear differential systems

Joelle Saade

05/09/2019 14:00

8. Becker’s conjecture on Mahler functions

Frédéric Chyzak

05/09/2019 15:00

In 1994, Becker conjectured that if $F(z)$ is a $k$-regular power series, then there exists a $k$-regular rational function $R(z)$ such that $F(z)/R(z)$ satisfies a Mahler-type functional equation with polynomial coefficients where the initial coefficient satisfies $a_0(z)=1$. In this work, we prove Becker’s conjecture in the best possible form; we show that the rational function $R(z)$ can...

2. Integration on Darbouxian foliations

M. Thierry Combot

05/09/2019 16:20

Consider a Darbouxian function $f=F_0+\sum {\lambda }_i\ln F_i$ with $F_i$ rational functions in two variables, and the foliation of curves ${\mathcal{C}}_h=\{f(x,y)=h\}$. We consider the problem of symbolic integration of a rational function $G$ along ${\mathcal{C}}_h$. If the monodromy of the integral satisfies a differential equation in $h$, then it is linear with constant coefficients, and the...

10. q-Stokes phenomenon of basic hypergeometric equations

Yousuke Ohyama

05/09/2019 17:20

We study connection formula on basic hypergeometric equations. Some solutions are represented by divergent power series. Some are divergent basic hypergeometric series, and others are non-hypergeometric type series. We need several q-analogues of the Laplace transformation for different types of divergent power series. This is a jointed work with Changgui Zhang.

3. Ax-Lindemann-Weierstrass theorem for the genus 0 Fuchsian groups

M. Guy Casale

06/09/2019 09:30

4. The asymptotic proprieties of solutions of a q-difference equation as q tends to a root of unity

Changgui Zhang

06/09/2019 11:00