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Speaker:

Nils Matthes
Affiliation:

U. Hamburg/MPIM
Date:

Wed, 2017-07-19 14:15 - 15:15
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar Following Enriquez and Brown-Levin, we study "iterated period integrals" (also called "elliptic analogs of multiple zeta values") on a once-punctured, complex elliptic curve. They are constructed from a certain meromorphic Jacobi form $F$, first studied by Kronecker in the 19th century and rediscovered in the late 1980s by Zagier. Similar to classical period integrals, iterated period integrals have a Hodge-theoretic interpretation: they describe the mixed Hodge structure on the pro-unipotent completion of the fundamental group of the curve. In this talk, we show that iterated period integrals can be rewritten as linear combinations of iterated integrals of Eisenstein series (in the sense of Manin and Brown). Surprisingly, not all linear combinations of iterated Eisenstein integrals can occur this way: there is an obstruction coming from cohomology classes of the modular curve $X(1)$. If time permits, we will also mention how Hain-Matsumoto's theory of "universal mixed elliptic motives" explains this phenomenon.

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