Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics

Abstract

Atiyah and Bott used equivariant Morse theory applied to the Yang-Mills functional to calculate the Betti numbers of moduli spaces of vector bundles over a Riemann surface, rederiving inductive formulae obtained from an arithmetic approach which involved the Tamagawa number of SL_n. This article surveys this link between Yang-Mills theory and Tamagawa numbers, and explains how methods used over the last three decades to study the singular cohomology of moduli spaces of bundles on a smooth complex projective curve can be adapted to the setting of A^1-homotopy theory to study the motivic cohomology of these moduli spaces.

Locations

• Bulletin of the London Mathematical Society - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View