# Algebraic Geometry Seminar

#### Zagier's conjecture on special values of zeta-functions and cluster geometry of polylogarithyms.

**Speaker:**
Alexander Goncharov, Yale

**Location:**
Warren Weaver Hall 317

**Date:**
Tuesday, May 14, 2019, 3:30 p.m.

**Synopsis:**

According to Zagier's conjecture, generalizeing the classcial Dirichlet formula for the residue of the Dedekind zeta-function zeta(F,s) of a number field F, the special values zeta(F,n) can be expressed via a determinant whose entries are classical n-logarithms evaluated at certain points. This conjecture has been proved for n=2,3,4, where the case n=4 was settled by the author and Daniil Rudenko a year ago.

It is a shadow of a much more general conjecture about the structure of the maximal Tate quotient of the motivic Galois group of an arbitrary field.

I will explain one of the ingredients of the proof: a surprising relationship between the polylogarithms and geometry of cluster varieties.