# Highest weight perverse sheaves

Given a topologically stratified space \( X \) and a perversity function \( p \) on it, one can build the category of \( p \)-perverse sheaves on \( X \) by considering the heart of a certain t-structure. Under suitable topological assumptions on \( X \) perverse sheaves are finite dimensional modules over a finite dimensional algebra independently on the chosen perversity function. It is then natural to ask under which further assumptions on the topology of the considered space perverse sheaves are highest weight. In this talk, based on ongoing joint work with Jon Woolf, I will explain some sufficient (topological) conditions on \( X \) which ensure that perverse sheaves are highest weight.