# On a certain class of linear relations among the multiple zeta values arising from the theory of iterated integrals

In this talk, we consider iterated integrals on a projective line minus generic four points and introduce a new class of linear relations among the MZVs, which we call confluent relations. We start with Goncharov’s notation for iterated integrals, review some basic notions and properties of iterated integrals, and define a class of relations among iterated integrals, which naturally arise as “solving differential equations step by step”. Confluent relations are defined as the limit of these relations when merging two out of the four punctured points. One of the significance of the confluent relations is that it is a rich family and seems to exhaust all the linear relations among the MZVs. As a good reason for this, we show that confluent relations imply the extended double shuffle relations as well as the duality relations. This is a joint work with Nobuo Sato at National Taiwan University.

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