### Periods of modular forms and relations in the fundamental Lie algebra of Universal Mixed Elliptic Motives

Pollack, A *(Princeton University)*

Wednesday 10 April 2013, 11:30-12:30

Seminar Room 1, Newton Institute

#### Abstract

Hain and Matsumoto have defined a category of so-called universal mixed elliptic motives, universal in the sense that such objects should be thought of as living over the moduli of all elliptic curves. They have shown that this category is neutral Tannakian. An interesting question then is understand explicitly the fundamental Lie algebra of this category. We make some progress in this direction, by proving a result about relations between a minimal set of generators for this Lie algebra. In particular, we find that periods of modular forms are closely connected to these relations. This work is closely related to older work of Schneps, and it also appears that there may be some connection to work of Gangl-Kaneko-Zagier.