Ramified and Unramified Motivic Euler Sums, Multiple t-, T- and S-Values

：徐策（安徽师范大学）
：2024-10-01 10:30
：海韵园行政楼C503

报告人：徐策（安徽师范大学）

时  间：2024年10月1日10:30

地  点：海韵园行政楼C503

内容摘要:

In this talk we shall consider a few variants of the motivic multiple zeta values of level two by restricting the summation indices in the definition of multiple zeta values to some fixed parity patterns. These include Hoffman's multiple t-values, Kaneko and Tsumura's multiple T-values, and the multiple S-values studied previously by the authors. By applying Brown and Glanois's descent theory on the motivic versions of these values we shall derive some criterion for when these values are ramified and unramified. Assuming Grothendieck's period conjecture, our results partially confirms a conjecture of Kaneko and Tsumura about when multiple T-values can be expressed as a rational linear combination of multiple zeta values (i.e., unramified) if their depth is less than four. Similar results are obtained for motivic multiple S-values. Further, we are able to generalize a result of Charlton to more families of unramified multiple t-values with unit components (i.e. component equal to 1). We propose some more unsolved problems at the end of the talk. This is a joint work with Jianqiang Zhao.  

个人简介：

徐策，硕士生导师，安徽师范大学数学与统计学院副教授。2020年博士毕业于厦门大学，曾在日本九州大学访学一年，师从Masanobu Kaneko教授。长期从事多重zeta值（Multiple zeta values, MZVs）及其相关变形的研究。主持国家自然科学基金（青年项目），安徽省自然科学基金（青年项目）和安徽省教育厅高校项目各1项。在《Mathematische Zeitschrift》、《Journal of Algebra》、《Forum Mathematicum》、《Advances in Applied Mathematics》、《Journal of Number Theory》《European Journal of Combinatorics》等期刊发表学术论文60余篇。

 

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