The inverse Galois problem for Cherednik algebras

The q-analogue of the wild fundamental group and the inverse problem of the Galois theory of q-difference equations

In previous papers, we defined $q$-analogues of alien derivations for linear analytic $q$-difference equations with integral slopes and proved a density theorem (in the Galois group) and a freeness theorem. In this paper, we completely describe the wild fundamental group and apply this result to the inverse problem in $q$-difference Galois theory. The new version contains an appendix on pronilpotent completion and the main result on the direct problem is made more precise. (Submitted for publication)

量子代数的刚性

Rigidity of quantum algebras

本文研究量子代数的刚性，证明一大类滤过量子化具有强刚性，并给出包络代数、有限W-代数、rational Cherednik代数及量子环面等多类量子代数的刚性、逆伽罗瓦问题和Picard群结构结果。