16-20 November 2020
IHES
Europe/Paris timezone

Renormalization Hopf Algebras and Gauge Theories: an Overview

16 Nov 2020, 15:00
50m
Marilyn and James Simons Conference Center (IHES)

Marilyn and James Simons Conference Center

IHES

35 route de Chartres, F-91440 Bures-sur-Yvette, France

Speaker

Prof. Walter van SUIJLEKOM (Radboud Universiteit Nijmegen)

Description

We give an overview of the Hopf algebraic approach to renormalization, with a focus on gauge theories. We illustrate this with Kreimer's gauge theory theorem from 2006 and sketch a proof. It relates Hopf ideals generated by Slavnov-Taylor identities to the Hochschild cocycles that are given by grafting operators.

In the second part of the talk I will briefly present Kreimer's unexpected influence on noncommutative geometry via my more recent research. In joint work with Teun van Nuland we uncover a rich structure of the spectral action functional. We express its Taylor expansion in an inner perturbation in terms of Yang-Mills and Chern-Simons forms integrated against even Hochschild and odd cyclic cocycles, respectively.

Presentation Materials