CRM: Centro De Giorgi

This is the old version of the CRM site. Please use the new site on the page crmdegiorgi.sns.it

logo sns
Fundamental Groups in Arithmetic and Algebraic Geometry

Motivic structures on completions of modular groups

speaker: Richard Hain (Duke University )

abstract: Mapping class groups and their arithmetic analogues are fundamental groups of moduli spaces of curves. They can be built up from mapping class groups of genus 0 and 1. So, to understand the motivic structure of all mapping class groups, it should suffice to understand them in genera 0 and 1. The motivic structure of genus 0 mapping class groups is reasonably well understood, thanks to the work of Goncharov, Deligne and Brown. Genus 1 mapping class groups are (basically) modular groups. In this talk I will discuss motivic structures (Hodge and Galois) on completions of modular groups and their arithmetic analogues. These structures are remarkably rich due to the role of modular forms. I will conclude with a description of the theory of universal mixed elliptic motives. Much of this work is joint with Makoto Matsumoto.


timetable:
Fri 20 Dec, 10:30 - 11:30, Aula Dini
<< Go back