报告人简介：罗马，本科毕业于北京大学，2018年获得杜克大学数学博士，导师为Richard Hain，牛津大学数学研究所博士后。研究方向为代数几何和数论，目前对椭圆曲线模空间的基本群，代数De Rham理论感兴趣。研究成果发表在Algebra Number Theory，Trans. Amer. Math. Soc., J. Algebra.等知名国际数学期刊上。

报告摘要：I will discuss structural presentations for relative completions of mapping class groups. In higher genus cases with genus at least 3, presentations are known, and will be reviewed first. The genus 2 case is unknown, but we provide a partial solution. In this case, the generators are related to Collino cycles. This is a direct analogue of higher genus cases where generators are related to Ceresa cycles. As for relations, we provide evidence to generate them via arithmetic considerations, while in higher genus cases, relations are quite topological. This is joint work with Tatsunari Watanabe.