Séminaire Analyse Harmonique
Determinants of Laplacians: an approach via the Brownian loop soup
19
nov. 2024
nov. 2024
| Intervenant : | Pierre Perruchaud |
| Institution : | Université du Luxembourg |
| Heure : | 14h00 - 15h00 |
| Lieu : | Salle 2L8 |
In the standard model of particle physics, the main mathematical protagonists are sections of vector bundles (modelling e.g. the electron field) and connections on these bundles (modelling e.g. the electromagnetic potential). We will introduce these objects, and discuss a simplification of this model where the determinant of some Laplace operator plays a central role.
Our main contribution, and the bulk of the talk, is a rewriting of this determinant in terms of the so-called Brownian Loop Soup. We will shy away from proofs, focusing instead on introducing and providing intuition for gauge theory, the Brownian Loop Soup, and the Gaussian free field.