Seminar on W-algebras and Integrable Systems

[Boris Dubrovin]

Dear All,

This week meetings of the Seminar on W-algebras and Integrable Systems
will take place on

1) Wednesday, July 13, 14:30-16:00, Room 136 of SISSA Main Building

Speaker: Sylvain Carpentier (MIT)

Title: Integrable rational differential operators

Abstract: We will discuss sufficient and necessary conditions for a rational differential operator L=AB^{-1} to generate a Lenard-Magri scheme of integrability. Provided that L can be applied infinitely many times  to a root function, the functions in the hierarchy pairwise commute if and only if L lies in a class
of rational operators that we call integrable. If we assume moreover that L is weakly non-local and preserves a Z/2Z-grading of the algebra of functions, we show that one can always construct an integrable  hierarchy starting from any function in Ker B.

(this is just a reminder);



2) Friday, July 15, 11:00 - 12:30, Room 136 of SISSA Main Building

Speaker: Daniele Valeri (Tsinghua University)

Title: Classical W-algebras

Abstract: We will give the definition of the classical W-algebras W(g,f),  where g is a Lie algebra and f in g is a nilpotent element, in the framework of Poisson vertex algebras. We will discuss some sufficient conditions on the nilpotent element f which guarantee the existence of generalized Drinfeld-Sokolov hierarchies for classical W-algebras. In the case of g=gl_N, generalized Drinfeld-Sokolov hierarchies are constructed for arbitrary nilpotent elements using the notion of Adler type pseudodifferential operators.

Everybody is welcome.

Boris Dubrovin