Professor at the LPSM (Laboratoire de Probabilités, Statistique et Modélisation), at Sorbonne Université
Member of the Dynamics, probability, geometry team
Mail : firstname.lastname@sorbonne-universite.fr
Postal address : Sorbonne Université, LPSM – 4, place Jussieu – F-75005 Paris
Office : 16-26 120

In Master 1 : Probabilités approfondies – UE MU4MA011
In Master 2 : Convergence de mesures, Grandes déviations, Percolation (CGP)

I am deputy director of the Master of mathematics, in charge of the M1.

My work is related, more or less directly, to the probabilistic study of gauge theories, on a two-dimensional Euclidean space-time or on graphs. I have studied the Yang-Mills measure on surfaces, its semi-classical limit, its “large N” limit. In the last few years, I have been interested in the geometry and statistical physics of graphs with a vector bundle and a connection.

In my work, I use parts of the differential geometry of principal bundles, the representation theory of classical compact Lie groups and symmetric groups, the theory of large random matrices, non-commutative probability, in particular free probability, the theory of determinantal point processes. I have occasionally used potential theory in the complex plane and large deviations.

Among the things I have not yet worked with, I am particularly interested in Chern–Simons theory and the Wess–Zumino–Witten model, quantum deformations of the Yang–Mills measure, the theory of regularity structures.

• On the mean projection theorem for determinantal point processes, avec Adrien Kassel. [ arXiv:2203.04628 ]

• Determinantal probability measures on Grassmannians. To appear in Ann. Inst. Henri Poincaré D, avec Adrien Kassel. [ arXiv:1910.06312 ]

• Covariant Symanzik identities. Probability and Mathematical Physics, 2 (2021) no. 3, 419–475, avec Adrien Kassel.

• Two-dimensional quantum Yang–Mills theory and the Makeenko–Migdal equations. Frontiers in analysis and probability, 275–325, Springer (2020). [ arXiv:1912.06246 ]

• A colourful path to matrix-tree theorems. Algebraic Combinatorics, 3 (2020), no. 2, 471–482 , avec Adrien Kassel. [ arXiv:1903.02491 ]

• Four chapters on low-dimensional gauge theories. Stochastic geometric mechanics, Springer Proc. Math. Stat. 202 (2017), 115–167, avec Ambar N. Sengupta.

• The master field on the plane. Astérisque, 388 (2017). [ arXiv:1112.2452 ]

• The number of prefixes of minimal factorisations of a cycle. Electron. J. Combin, 23 (2016) no. 3.

• On The Douglas–Kazakov phase transition. ESAIM: Proc., 51 (2015), avec Mylène Maïda.

• Topological quantum field theories and Markovian random fields. Bull. Sci. Math., 135 (2011) no. 6-7, 629–649.

• A continuous semigroup of notions of independence between the classical and the free one. Ann. Prob., 39 (2011) no. 3, 904–938, avec Florent Benaych-Georges. [ arXiv:0811.2335 ]

• Central limit theorem for the heat kernel measure on the unitary group. J. Funct. Anal, 259 (2010) no. 12, 3163–3204, avec Mylène Maïda. [ arXiv:0905.3282 ]

• Two-dimensional Markovian holonomy fields. Astérisque, 329 (2010). [ arXiv:0804.2230 ]

• Schur–Weyl duality and the heat kernel measure on the unitary group. Adv. Math., 218 (2008) no. 2, 537–575. [ arXiv:math/0703690 ]

• Differential equations driven by rough paths, Lecture Notes in Mathematics Vol. 1908. Notes du cours de Terry J. Lyons à l'école d'été de Saint-Flour en 2004. Rédigées avec Michael J. Caruana.

• Large deviations for the two-dimensional Yang–Mills measure, Actes de la conférence Stochastic Analysis in Mathematical Physics (Lisbonne 2006). World Scientific.

• Discrete and continuous Yang–Mills measure for non-trivial bundles over compact surfaces. Probab. Theory Related Fields, 136 (2006) no. 2, 171–202. [ arXiv:math-ph/0501014 ]

• Large deviations for the Yang–Mills measure on a compact surface. Comm. Math. Phys., 261 (2006) no. 2, 405–450, avec James R. Norris. [ arXiv:math-ph/0406027 ]

• Wilson loops in the light of spin networks. J. Geom. Phys., 52 (2004) no. 4, 382–397. [ arXiv:math-ph/0306059 ]

• Yang–Mills measure on compact surfaces. Mem. Amer. Math. Soc., 166 (2003) no. 790, xiv+122 pp. [ arXiv:math/0101239 ]

• Comment choisir une connexion au hasard ? Séminaire de Théorie Spectrale et Géométrie Vol. 21 (2002–2003), 61–73. Accès au texte.

• Construction et étude à l'échelle microscopique de la mesure de Yang–Mills sur les surfaces compactes. C. R. Math. Acad. Sci. Paris, 330 (2000) no. 11.

• Florent Benaych-Georges
• Michael J. Caruana
• Adrien Kassel
• Terry J. Lyons
• Mylène Maïda
• James R. Norris
• Ambar N. Sengupta