Два доклада Ивана Лосева

25 августа 2016 г. (четверг), 16:30, ауд. 212

Cacti and cells

Cells (left, right and two-sided) are subsets in a Weyl group W that play
an important role in several branches of Lie Representation theory.
The cactus group of W is a group that should be thought as a crystal analog
of the braid group. I will produce an action  the cactus group on W that behaves
nicely on cells. This should be  thought as a Weyl group analog of Kashiwara's
crystals. The action comes  from the categorical actions of the braid group on
the BGG categories O. This talk is based on
http://arxiv.org/abs/1506.04400



26 августа 2016 г. (пятница), 15:30, ауд. 212

Deformations of symplectic singularities and the orbit method.
Symplectic singularities were introduced by Beauville in 2000.
These are especially nice singular Poisson algebraic varieties that
include symplectic quotient singularities and the normalizations
of orbit closures in semisimple Lie algebras. Poisson deformations
of conical symplectic singularities were studied by Namikawa who proved that
they are classified by  points of a vector space. Recently I have
proved that quantizations of  conical symplectic singularities
are still classified by the points of the same vector spaces. I will
explain these results and then apply them to establish a version of
Kirillov's orbit method for semisimple Lie algebras. The talk is based
on http://arxiv.org/abs/1605.00592