Algebra Seminar: Bapat -- Perverse sheaves on hyperplane arrangements and gluing

Asilata Bapat (Australian National University) 

Friday 3 August, 12-1pm, Place: Carslaw 375 

Title: Perverse sheaves on hyperplane arrangements and gluing 

Abstract: A hyperplane arrangement cuts up a vector space into several pieces. The
combinatorics and topology of this subdivision is encoded in an associated abelian
category of perverse sheaves. This category has an alternate algebraic description due
to Kapranov and Schechtman, in terms of representations of a quiver with relations. I
will first explain a version of this description. I will then focus on gluing, or
"recollement", which is a recipe to reconstruct the category of perverse sheaves on a
space from an open subset and its complement. I will describe how recollement on the
above category of perverse sheaves translates to the category of quiver
representations.