*Grothendieck-Teichmueller Theory and Multiple Zeta Values*workshop on April 8, 2013 at the Newton Institute for Mathematical Sciences. This workshop was part of the

*Grothendieck-Teichmueller groups, Deformation and Operads*program held at the Newton Institute for Mathematical Sciences at Cambridge University (United Kindom) January 3 to April 26, 2013.

Link to the video of the talk given by Ivan Horozov on April 8, 2013⇨

The title of the lecture is *Multiple Dedekind Zeta Functions*. "In this talk," writes Horozov, "I define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider MDZV as a number theoretic generalization of Euler's multiple zeta values. Over imaginary quadratic fields MDZV capture, in particular, multiple Eisenstein series (Gangl, Kaneko and Zagier). I will give an analogue of multiple Eisenstein series over real quadratic field and an alternative definition of values of multiple Eisenstein-Kronecker series (Goncharov). Each of them is a special case of multiple Dedekind zeta values. MDZV are interpolated into functions that we call multiple Dedekind zeta functions (MDZF). I show that MDZF have integral representation, can be written as infinite sum, and have analytic continuation. If time permits, I will give explicitly the value of a multiple residue of certain MDZF over a quadratic number field at the point (1,1,1,1)."

Link to the Grothendieck-Teichmueller Groups, Deformation and Operads program page⇨

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