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SUMMARY:Yang–Mills theory for multiplicative Ehresmann connections
DTSTART:20261106T130000Z
DTEND:20261106T140000Z
DTSTAMP:20261112T050900Z
UID:indico-event-17605@indico.math.cnrs.fr
CONTACT:athomas@math.univ-lyon1.fr
DESCRIPTION:Speakers: Zan Grad (Leuven)\n\nYang–Mills theory is a framew
 ork for finding connections with minimal curvature\, using variational cal
 culus. This talk is about a generalization of Yang–Mills theory\, from p
 rincipal bundles (viewed as transitive groupoids) to possibly non-transiti
 ve Lie groupoids and Lie algebroids. In our framework\, principal bundle c
 onnections are replaced with the more general notion of (infinitesimal) mu
 ltiplicative Ehresmann connections\, which are a type of connections compa
 tible with the structure of a Lie groupoid (or algebroid) introduced by Fe
 rnandes & Mărcuţ. Our action functional for such connections includes a 
 curvature 3-form contribution\, alongside the usual curvature 2-form term\
 , and the resulting variational problem is naturally constrained by a coho
 mological condition. We present the associated Euler–Lagrange equations\
 , demonstrate the gauge invariance of the solution space\, and relate the 
 global and infinitesimal theory via the van Est map. As an important appli
 cation\, we obtain a Yang–Mills theory for bundle gerbes.\n\nhttps://ind
 ico.math.cnrs.fr/event/17605/
LOCATION:112 (Bat. Braconnier)
URL:https://indico.math.cnrs.fr/event/17605/
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