Title: Introduction to Principaloid Bundles
Speaker: Thomas Strobl
Affiliation: University of Lyon
Time: July 15, 2025, 16:30-17:30
Venue: Seminar Room 5, Mathematics Building, Jilin University
Abstract:
Standard gauge theories are based on principal G-bundles and associated bundles, where G is a (finite-dimensional) Lie group. However, there are gauge theories that do not fit within this framework, including the Poisson sigma model, gauged standard sigma models with a metric that does not admit isometries, and curved Yang-Mills-Higgs gauge theories. For this purpose we introduce principaloid bundles P, which are based on structure Lie groupoids. These are honest fiber bundles and as such fundamentally different from principal groupoid bundles. We show that ordinary principal bundles, their associated bundles, as well as general fiber bundles are particular examples. We study connections on them, their gauge transformations, and construct the Atiyah groupoid of P, which governs its symmetries. This is joint work with Rafal Suszek.
Speaker's Biography:
Thomas Strobl is a professor in the mathematics department at the University of Lyon. His work as a mathematical physicist is mainly concerned with geometric and algebraic aspects of sigma models and gauge theories. In 1993, during his PhD thesis and together with P. Schaller, he discovered the Poisson Sigma Model; it was used later by M. Kontsevich to obtain his famous quantization formula. In 2015 he and A. Kotov introduced a generalisation of Yang-Mills gauge theories to the Lie algebroid setting. In total, in his career he authored more than 60 scientific articles.
