Title: Full strong exceptional collections on rank-two linear GIT quotients
Abstract: A full strong exceptional collection is an important structure to have on a derived category with many useful implications. For instance, such a collection produces a basis for the Grothendieck group and a tilting object. In this talk, we will discuss the existence of full strong exceptional collections consisting of vector bundles on certain linear GIT quotients by a split reductive group G of rank two. These vector bundles will come from irreducible G-representations whose weights lie in a particular “window” in the weight space of G. This is based on joint work with Daniel Halpern-Leistner.