PIRSA:19050001

Multiple zeta values in deformation quantization

Pym, B. (2019). Multiple zeta values in deformation quantization. Perimeter Institute. https://pirsa.org/19050001

Pym, Brent. Multiple zeta values in deformation quantization. Perimeter Institute, May. 06, 2019, https://pirsa.org/19050001 

          @misc{ pirsa_PIRSA:19050001,
            doi = {10.48660/19050001},
            url = {https://pirsa.org/19050001},
            author = {Pym, Brent},
            keywords = {Mathematical physics},
            language = {en},
            title = {Multiple zeta values in deformation quantization},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {may},
            note = {PIRSA:19050001 see, \url{https://pirsa.org}}
          }

Brent Pym

McGill University

Talk number
PIRSA:19050001
Collection
Talk Type
Subject
Abstract

In 1997, Kontsevich gave a universal solution to the "deformation quantization" problem in mathematical physics: starting from any Poisson manifold (the classical phase space), it produces a  noncommutative algebra of quantum observables by deforming the ordinary multiplication of functions.  His formula is a Feynma  expansion, involving an infinite sum over graphs, weighted by volume integrals on the moduli space of marked holomorphic disks. The precise values of these integrals are currently unknown.  I will describe recent joint work with Banks and Panzer, in which we develop a theory of integration on these moduli spaces via suitable sheaves of polylogarithms, and use it to prove that Kontsevich's integrals evaluate to integer-linear combinations of special transcendental constants called multiple zeta values, yielding the first algorithm for their calculation.