Algebraic de Rham theory for relative completion of $\mathrm{SL}_2(\mathbb{Z})$

Number Theory Seminar

Ma Luo (Duke University)

Wednesday, December 6, 2017 -
3:15pm to 4:15pm
Location: 
119 Physics

In this talk, I will first review relative (unipotent) completions of discrete groups in general, and $\mathrm{SL}_2(\mathbb{Z})$ in particular. We then develop an explicit $\mathbb{Q}$-de Rham theory for the relative completion of $\mathrm{SL}_2(\mathbb{Z})$, which enables us to construct iterated integrals of modular forms of the second kind that provide its periods. Following Francis Brown, these periods are called `multiple modular values'. They contain periods of modular forms.

Last updated: 2017/12/10 - 4:21am