Non-crossing partitions and combinatorics, from random matrices to free cumulants to parking functions

Philippe Biane (U Gustave Eiffel, Champs-sur-Marne)

Feb 17. 2025, 09:30 — 10:15

In the first two lectures I will define free cumulants, using non-crossing partitions, and explain how this definition emerges naturally from the theory of random matrices and integration on unitary groups.  The Schur-Weyl duality between symmetric groups and unitary groups plays an important role. I will then explain the basics of free probability and how the combinatorics of non-crossing partitions and free cumulants allows to relate it to random matrix theory.

In the last lecture I will take on another topic, the combinatorics of maximal chains in the non-crossing partition lattice, which relates non-crossing partitions, parking functions, and the Tamari lattice.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability (Workshop)
Organizer(s):
Adrian Celestino Rodriguez (TU Graz)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
James Mingo (Queen's U, Kingston)
Martin Rubey (TU Vienna)
Eleni Tzanaki (U of Crete)
Yannic Vargas (CUNEF U, Madrid)