The monodromy map from differential systems to character variety is generically immersive

Deformations of polynomials, boundary singularities and monodromy

We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain families of boundary singularities along the hyperplane at infinity.

亏格6中Prym映射的单值性与半典范铅笔

Monodromy of the Prym map and semicanonical pencils in genus 6

本文证明了亏格6中限制于奇半典范铅笔除子的Prym映射是双有理的，其单值群为Weyl群$WD_5$，并揭示了模空间中其他除子的次数及几何性质。

Tannakian单束群的等分布性

Equidistribution for Tannakian monodromy groups

本文通过 Tannakian 类别方法，证明了 Tannakian 单束群的等分布定理，并研究了指数和的分层以及相关消失定理。

超奇异阿贝尔曲面在 $\mathbb{Q}_p$ 上的单值群

Monodromy Groups of Supersingular Abelian Surfaces over $\mathbb{Q}_p$

本文对素数p≥7，参数化了Q_p上超奇异好约化阿贝尔曲面的p-adic Tate模的过滤φ-模，并由此确定了相关p-adic表示的单值群的单位分支（直到Q_p-同构），分析了其在模空间中的p-adic分布，证明单位分支一般同构于GL_2 ×_det GL_2。

Alternating groups and rational functions on surfaces

Let X be a smooth complex projective surface. We prove that for any sufficiently big m there exists a rational dominant map f from X into a complex rational ruled surface Y, such that f is generically finite of degree m and has monodromy the alternating group Am.

对称三次曲面的伽罗瓦群

Galois Groups of Symmetric Cubic Surfaces

本文提出用认证数值计算计算三次曲面族的伽罗瓦群（即27条直线的单值群），应用于$S_5$不变族发现其远小于Weyl群$W(E_6)$，并计算判别式及推广到四次曲面。