Séminaire du Cirget: «Multiple zeta values in deformation quantization»
Conférencier: Brent Pym, McGill
Résumé/Abstract: A famous 1997 formula of Kontsevich gives 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. The formula is an example of a Feynman 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.
Date / heure
- Département de mathématiques
- Centre interuniversitaire de recherches en géométrie et topologie (CIRGET)