Tuesday, July 20, 2021
David Fernández (Bielefeld),
Euler continuants in noncommutative quasi-Poisson geometry
Since their introduction in 1764 by Euler to study the numerators and
denominators of continued fractions, Euler continuants have become
essential in mathematics, appearing in diverse branches of
mathematics. In representation theory, Boalch used Euler continuants
to study certain wild character varieties, which can be described as
quiver varieties attached to the quiver Γn with two vertices
and n equioriented arrows. Interestingly, they carry a
(nondegenerate) Poisson structure.
As a part of our program to understand wild character varieties in
terms of Van den Bergh's noncommutative Poisson geometry, in this talk
I shall explain how the abovementioned Poisson structure can be
explained using an explicit Hamiltonian double quasi-Poisson structure
on the path algebra of Γn, which is such that the Euler
continuants are multiplicative moment maps. In addition, we will
discuss its relationship with the celebrated Flaschka-Newell bracket.
This is a joint work with Maxime Fairon (Glasgow).