The ellipsitomic KZB associator and elliptic MZVs at torsion points

The universal elliptic KZB connection has a twisted (or cyclotomic) counterpart. This is a at
connection de ned 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 sl2, 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 coe cients of this associator. Some parts of the
results come from a joint work with Damien Calaque.
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