# Journées du GDR EFI 2022

Sep 12 – 14, 2022
Toulouse
Europe/Paris timezone

## The Galois group of irregular $q$-difference equations

Sep 12, 2022, 2:30 PM
40m
Toulouse

#### Toulouse

Amphithéâtre Laurent Schwartz, Bat 1R3, UPS

Jacques Sauloy

### Description

The Galois group of irregular $q$-difference equations with integral slopes was described by Ramis and Sauloy, along with a Riemann-Hilbert correspondence, based on classification results by Ramis-Sauloy-Zhang. The complete determination of a discrete Zariski-dense subgroup, the "wild fundamental group" allowed to solve the inverse problem in that case. For arbitrary slopes, the wild fundamental group has also been determined, but no corresponding progress has been made for the inverse problem. The talk will be purely descriptive.

### Presentation materials

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