Résumé : The advent of tensor models (TM) in physics (quantum gravity theory) has produced eminent results that put them at the center of discussions in the early 90s. TM generalize matrix models producing the famous random maps whose continuum limit is known as the Brownian sphere. They therefore define useful tools for understanding discrete and random geometries in dimension greater than or equal to 3 as well as their continuum limits. My research, during the last past years, focused on their extension in a field theoretic setting. We discover several crucial features of these field theories, both at the mathematical and physical level, and for all results, combinatorics plays a pivotal role. Combinatorics indeed illustrates the fertile link between mathematical physics, algebra and computer science that this thesis reports.

Plan of the presentation:
Intro
1 Graphs and stranded graphs
2 Tensor Field Theories: Renormalization Group analysis
3 Polynomial invariants for weakly colored graphs
4 Enumeration, topological and algebraic structures on tensor graphs
5 A lattice interpretation of the Kronecker coefficient
Conclusion

Jury
Frédérique Bassino (Université Sorbonne Paris Nord)
Olivier Bodini (Université Sorbonne Paris Nord)
Robert De Mello Koch (University of Witwatersrand), rapporteur.
Harald Grosse (Universität Wien), rapporteur.
Maxim Kontsevich (Institut des Hautes Etudes Scientifiques)
Manfred Salmhofer (Universität Heidelberg)
Gilles Schaeffer (Ecole Polytechnique), rapporteur.
Raimar Wulkenhaar (Westfälischen Wilhelms-Universität), rapporteur.

 [vidéo]

Dernière modification : Monday 18 March 2024

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr