Oliver Schnetz: Proof of the zig-zag conjecture

Abstract:

In quantum field theory primitive Feynman graphs give---via the period map---rise to renormalization scheme independent contributions to the beta function. While the periods of many Feynman graphs are multiple zeta values there exists the distinguished family of zig-zag graphs whose periods were conjectured in 1995 by D. Broadhurst and D. Kreimer to be certain rational multiples of odd single zetas.

In joint work with F. Brown it was possible in 2012 to prove the zig-zag conjecture using the theory of graphical functions, single-valued multiple polylogarithms and a theorem by D. Zagier on multiple zeta values of the form zeta(2,...,2,3,2,...,2).