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Jianqiang Zhao : Arithmetic and Geometry of Multiple Polylogarithms

In this talk I will describe a proof of a conjecture made by Beilinson et al concerning the motivic complex in the weight three case. Then I will explain a new way to define the analytic continuation of the multiple polylogarithms which provides an appproach to defining the good variations of mixed Hodge-Tate structures associated to the multiple polylogarithms explicitly. As an application I will define the single-valued real analytic version of these multi-valued functions and which should be connected to the special values of multiple Dedekind zeta functions over general number fields.

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