Xiyan Zhong

activity

20242026

collaborators

5 papers

math.GT2026

Rigidity of the period map up to finite covers

Xiyan Zhong

We first give a complete classification of bi-affine representations of mapping class groups of surfaces with finitely many boundary components or punctures. We also show that ever…

math.GT2026

Abelianization of Symmetric Mapping Class Groups

Xiyan Zhong

Let $S \to S$ be an unbranched regular $p$ -fold cyclic cover of a closed orientable surface $S$ of genus $g$ . Two natural groups are associated to this cover. The first…

math.AG2025

Stable cohomology of universal character varieties

Ishan Banerjee, Faye Jackson, Anne Larsen +2

We study the universal PGL_n character variety over M_g whose fiber over a point [C] is the space of PGL_n-local systems on the curve C. We use nonabelian Hodge theory and properti…

math.GT2025

Linear representations of the mapping class group of dimension at most $3 g - 3$

Julian Kaufmann, Nick Salter, Zhong Zhang +1

We classify representations of the mapping class group of a surface of genus $g$ (with at most one puncture or boundary component) up to dimension $3 g - 3$ . Any such representation i…

math.GT2024

Prym Representations and Twisted Cohomology of the Mapping Class Group with Level Structures

Xiyan Zhong

We compute the twisted cohomology of the mapping class group with level structures, with coefficients in the $r$ -tensor powers of the Prym representations for any positive integer…

Rigidity of the period map up to finite covers

Abelianization of Symmetric Mapping Class Groups

Stable cohomology of universal character varieties

Linear representations of the mapping class group of dimension at most 3g−3

Prym Representations and Twisted Cohomology of the Mapping Class Group with Level Structures

Linear representations of the mapping class group of dimension at most $3 g - 3$