Integrable systems, random matrices, complex geometry and analysis

Team members


Research topics

  • The study of random matrices, very active domain of research, which has applications in combinatorics, number theory, physics, statistics and telecommunication.
  • Asymptotic analysis of orthogonal polynomials and Hankel, Toeplitz and Fredholm determinants, Riemann-Hilbert problems.
  • Integrable differential equations, such as Painlevé equations (solutions to them are called the special function of the 21st century) and the Korteweg-de Vries equation (which describes shallow water waves).
  • Diffusion processes, such as Brownian motion, and determinantal point processes.
  • Equations defining abelian surfaces, tau functions and representations of the Virasoro algebra and W-algebras.

Representative publications

  • M. Adler, Mark, K. Johansson, Kurt, and P. van Moerbeke, Double Aztec diamonds and the tacnode process, Adv. Math. 252 (2014), 518–571
  • T. Claeys, T. Grava, and K. T-R McLaughlin, Asymptotics for the partition function in two-cut random matrix models, Comm. Math. Phys. 339, no. 2 (2015), 513-58
  • T. Claeys, A. Its, and I. Krasovsky, Higher order analogues of the Tracy-Widom distribution and the Painlevé II hierarchy, Comm. Pure Appl. Math. 63 (2010), 362-412
  • T. Claeys, A. Its, and I. Krasovsky, Emergence of a singularity for Toeplitz determinants and Painlevé V, Duke Math. Journal 160, no. 2 (2011), 207-262
  • T. Claeys and I. Krasovsky, Toeplitz determinants with merging singularities, Duke Math. Journal 164, no. 15 (2015), 2897-2987
  •  P. van Moerbeke, Random and integrable models in mathematics and physics. Random matrices, random processes and integrable systems, 3–130, CRM Ser. Math. Phys., Springer, New York, 2011.
  • L. Haine, E. Horozov, P. Iliev, The trigonometric Grassmannian and a difference W-algebra, Transformation Groups, Vol. 15, n°1 (2010), 92-114.
  • L. Haine, D. Vanderstichelen, A centerless Virasoro algebra of master symmetries for the Ablowitz-Ladik hierarchy, Symmetry, Integrability and Geometry: Methods and Applications, Vol. 9, 079 (2013), 42 pages.

Useful links

•    Séminaire GPP, Géométire, Physique, Probabilités.
•    PAI (Phase VII-18) DYGEST, Pôle d'attraction interuniversitaire, Dynamics, Geometry and Statistical Physics.
•    ERC (European Research Council), Projet CRAMIS.