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Laguerre ensemble, Hurwitz number and Weingarten functions

Massimo Gisonni
Institution: 
SISSA
Location: 
Please write to mgisonni@sissa.it to get an invitation via teams.
Schedule: 
Wednesday, March 25, 2020 - 14:30
Abstract: 
Weingarten functions are a special class of maps on the symmetric group that arise naturally dealing with integrals over the classical group of transformations (unitary, orthogonal and symplectic) with respect to their Haar measure. Initially studied through methods of representation theory, they turned out to be a useful tool both in combinatorics and random matrix theory.

In this (smart) talk we will go through their construction and main properties, and see how they can be applied in the problem of determining the correlators of unitarily invariant matrix ensembles. 

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