Asymptotic representation theory and Riemann-Hilbert problem

量子斯托克斯矩阵与量子Riemann-Hilbert-Birkhoff映射

Quantum Stokes matrices and quantum Riemann-Hilbert-Birkhoff maps

本文引入非交换亚纯线性常微分方程组（极点阶数为p+1）的量子斯托克斯矩阵，证明其满足量子交换关系，并解释为Riemann-Hilbert-Birkhoff映射的形变量子化。

The higher Riemann-Hilbert correspondence and principal $2$-bundles

In this note we show that the holonomies for higher local systems provided by the higher Riemann-Hilbert correspondence coincide with those associated to principal $2$-bundles where both formalisms meet.

复切触流形的微局部黎曼-希尔伯特对应

The microlocal Riemann-Hilbert correspondence for complex contact manifolds

本文在复切触流形上建立了微局部化D-模与反常微层之间的黎曼-希尔伯特对应，统一了Kashiwara的范畴层构造与作者新近的反常微层理论。

Quiver $\mathscr{D}$-modules and the Riemann-Hilbert correspondence

In this paper, we show that every regular singular $\mathscr{D}$-module in $\mathbb{C}^n$ whose singular locus is a normal crossing is isomorphic to a quiver $\mathscr{D}$-module - a $\mathscr{D}$-module whose definition is based on certain representations of the hypercube quiver. To be more precise we give an equivalence of the respective categories. Our definition of quiver $\mathscr{D}$-modules is based on the one of Khoroshkin and Varchenko. To prove the equivalence, we use an equivalence by Galligo, Granger and Maisonobe for regular singular $\mathscr{D}$-modules whose singular locus is a…

对于亚历山大复形的Riemann-Hilbert对应关系

Riemann-Hilbert correspondence for Alexander complexes

本文通过相对正则紧致D-模建立了亚历山大复形的Riemann-Hilbert对应关系，并利用Bernstein-Sato理想零点得到其相对支撑的公式。