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

## root

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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.

• CategoryNumber Theory
• Duration: 01:34:40
• Date:  December 6, 2017 at 3:10 PM
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