Multiple zeta values in deformation quantization

Brent Pym (University of Edinburgh)

Wednesday 27th June, 2018 16:00-17:00 Maths 110

Abstract

In 1997, Maxim Kontsevich gave a universal formula for the quantization of Poisson brackets.  It is an example of a perturbative expansion in quantum field theory, and as such, its coefficients are given by certain high-dimensional period integrals associated to graphs.  The difficulty of these integrals is a substantial barrier to explicit calculations, even in simple examples.  I will describe forthcoming joint work with Banks and Panzer, in which we give an algorithm for the exact evaluation of these integrals in terms of special transcendental constants called multiple zeta values, building on Francis Brown's study of the periods of the moduli space of genus zero curves.

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