Project C4: Counting points on quiver Grassmannians
Project C4 lies at the intersection between algebraic geometry, representation theory of algebras and homological algebra. The goal is to define and study subobject Grassmannians of (certain) exact categories. Their geometric properties, in particular of models over the integers, will be investigated to obtain information on their point counting functions over finite fields and on their cohomology. This will be of great use for Hall algebras of exact categories and for exact categories with cluster structure.