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SUMMARY:Sylvain Lacroix: Finite N precursors of the free cumulants
DTSTART:20260114T130000Z
DTEND:20260114T140000Z
DTSTAMP:20260425T084300Z
UID:indico-event-15744@indico.math.cnrs.fr
DESCRIPTION:In this talk\, I will discuss various properties of a family o
 f finite N precursors of the free cumulants. They are polynomials on the s
 pace of NxN matrices\, invariant under conjugations and extracted from the
  so-called HCIZ integral. Their main feature is their additivity with resp
 ect to the average over sums of U(N)-conjugacy orbits. Moreover\, they adm
 it natural expansions in terms of Newton and Schur polynomials\, related t
 o the representation theory of the unitary and symmetric groups and recove
 ring a previous construction by Capitaine and Casalis. I will further disc
 uss their large N limit\, which yields the free cumulants\, with 1/N² cor
 rections expressed in terms of Hurwitz numbers. Finally\, expanding on the
  main additivity property of these objects\, I will describe the behaviour
  of general U(N)-invariant polynomials under sums of conjugacy orbits. Thi
 s talk is based on arXiv:2508.21483\, in collaboration with Jean-Bernard Z
 uber.\n\nhttps://indico.math.cnrs.fr/event/15744/
URL:https://indico.math.cnrs.fr/event/15744/
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