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Mini-Workshop: Elliptic Multiple Zeta Values and Mixed Elliptic Motives

This is supported by JSPS KAKENHI JP18H01110.

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Date

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28 (Sat). July. 2018.
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## Organizer

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Hidekazu Furusho (Nagoya University)
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Place

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Rm A428, Science Building A (not
Math Building!),
Nagoya University
(access).
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Program

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28 (Sat). July. 2018.
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13:30-14:30
Martin Gonzalez (IMJ, Paris),
On the ellipsitomic KZB associator

15:00-16:00
Nils Matthes (Kyushu Univ),
An algebraic characterization of the Kronecker function

16:30-17:30
Kenji Sakugawa (RIMS, Kyoto),
On mixed elliptic motives over modular curves

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Abstracts

Martin Gonzalez (IMJ, Paris)

Title: On the ellipsitomic KZB associator

Abstract:
The universal elliptic KZB connection has a twisted (or cyclotomic) counterpart. This is a flat
connection defined on a G-principal bundle over the moduli space of elliptic curves with n marked
points and a (M,N)-level structure. Here the Lie algebra associated to G is constructed from a
twisted elliptic Kohno-Drinfeld Lie algebra, the Lie algebra $\frak{sl}_2$, and a twisted derivation algebra
controlling the algebraic information of some modular forms. After presenting this connection I
will retrieve an ellipsitomic (or twisted elliptic) KZB associator from its monodromy and elliptic
multiple-zeta values at torsion points from the coefficients of this associator. Some parts of the
results come from a joint work with Damien Calaque.

Nils Matthes (Kyushu Univ)

Title: An algebraic characterization of the Kronecker function

Abstract:
Classical multiple zeta values can be written as iterated integrals of the differential forms $\frac{dz}{z}$ and $\frac{dz}{z-1}$. In a similar vein, elliptic multiple zeta values are defined as iterated integrals of (Laurent coefficients of) the form $F_{\tau}(\xi,\alpha)d\xi$ where $F_{\tau}$ is the Kronecker function (viewed as a Laurent series in $\alpha$).

In this talk, we characterize the Kronecker function using the Fay identity which is an elliptic analog of the partial fraction identities. If time permits, we give a similar characterization of the generating series of periods of modular forms studied by Zagier.

Kenji Sakugawa (RIMS, Kyoto)

Title: On mixed elliptic motives over modular curves

Abstract:
Let Y be a modular curve. The category of elliptic motives
over Y is a full subcategory of motivic local systems on Y in the sense
of Arapura. In this talk, we give a structure theorem of the Tannakian
fundamental group of this category. We also formulate a conjecture about
the p-adic etale realization of the Tannakian fundamental group and see
consequences of the conjecture. If time permits, I will explain a relation
between our category and the category of universal mixed elliptic motives
introduced by Hain and Matsumoto.

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