On some developments of the Stokes phenomenon (Q6606767)

Let \(M\) be the field of the meromorphic in the complex plane functions and \N\[\NY'=AY \tag{1}\N\] \Nbe a linear system of differential equations over \(M\). The key role in the description of the properties of the solutions of system (1) is played by the group differential autorphisms (differential Galois group), which is generated by autorphisms associated with the phenomenon of monodromy (Stokes), in regular (irregular) singular points. However, the calculation of this group is a very difficult task even in the case when system (1) has only two singular points regular and irregular. The paper is a review of several recent publications on this subject (see [\textit{X. Xu}, ``Closure of Stokes matrices. I: Caterpillar points and applications'', Preprint, \url{arXiv:1912.07196}; ``Representations of quantum groups arising from the Stokes phenomenon and applications'', Preprint, \url{arXiv:2012.15673}]).\N\NFor the entire collection see [Zbl 1531.53004].