EVENT DETAILS AND ABSTRACT

Title: Pre-talk: Connections between cubic fourfolds and hyperkähler manifolds via derived categories and Bridgeland stability
Speaker: Howard Nuer
Speaker Info: UIC
Brief Description:
Special Note:
Abstract:

In this introduction to my talk later on, I will introduce derived categories and Bridgeland stability conditions on them (and on more general triangulated categories). I will also discuss some of the general theory of cubic fourfolds and hyperkähler manifolds, as well as how these very different types of varieties are related. We will begin with classical constructions and move on to more recent relations via the Kuznetsov subcategory Ku(X) associated to a cubic fourfold X and the moduli spaces of Bridgeland stable objects in Ku(X) which give more examples of hyperkähler manifolds (though in the same deformation class). Time permitting, I’ll quickly review the classical definition of Donaldson-Thomas invariants for Calabi-Yau 3-folds to put in context the introduction of Piyaratne-Toda’s generalized DT invariants in the main talk.