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The goal of this workshop is to study the motivic approach to multiple zeta values (MZV's) including the recent advances due to Francis Brown. Basically, we will follow the presentation of Deligne [1]. We also refer to the foundational paper [2] for many preliminary facts concerning the motivic fundamental group of the projective line without three points and the appearence of MZV's in this context.
The program consists of 13 talks by 90 minutes. Each talk is provided with a detailed plan and description in the program below. All statements are expected to be proved or at least explained if the converse is not mentioned. For most of them, hints and ideas can be found in the program as well as in the cited papers. The speakers of the workshop are urged to start preparing their talks as soon as possible. The preparation assumes a creative work with making sort of exercises and compiling various sources and melting them under common notation and concepts of the workshop. The division of talks is tentative, and the speakers of adjacent talks can exchange some of the material to be covered. The difficulty of most talks is rather conecptual than technical. In case help is needed, everbody is welcome to contact: Joseph Ayoub or Sergey Gorchinskiy.
We assume familiarity with the following notions (some if this will be recalled in a pre-workshop, which is scheduled for Tuesday, 28.8., 10am-1pm and Wednesday, 29.8., 3-7pm in HG G19.2; the talks will be given by Brent Doran and Sergey Gorschinskiy): fundamental groups, path spaces, filtered vector spaces, Betti cohomology, (algebraic) de Rham cohomology, mixed Hodge structures, periods, linear algebraic groups (mostly unipotent), Lie algebras, Hopf algebras, dg-algebras, total complexes of bicomplexes. Some familiarity with simplicial and cosimplicial objects, sheaves and local systems will be certainly useful.