REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: One of the basic problems in microlocal geometry is to compute the characteristic cycle of a sheaf F on a complex manifold X which is perverse with respect to a given stratification. Kashiwara-Dubson formula expresses microlocal multiplicities of strata in terms of the Euler characteristics of stalks and some topological data of stratification which is called the Euler obstructions. In 1999 Mirkovic and Evens proved that for the affine Grassmannian with stratification by G[[z]]-orbits all nontrivial Euler obstructions vanish. I will talk about the joint work with M.Finkelberg where we generalise their argument to the stratification by symplectic leaves of affine algebraic Poisson variety endowed with a good enough reductive group action (such as Uhlenbeck spaces or more generally transversal slices in double affine Grassmanians). We also state the conjecture that connects a generic fiber of the microlocalisation of a sheaf with its hyperbolic stalks. If true for the case of affine Grassmanian it will introduce the local system of fiber functors and as a result the action of braid group on the category of G[[z]]-equivariant perverse sheaves on Gr.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu