Algebra/Topology seminar

Speaker: Zhaoting Wei (Kent State University-Geauga)

Title: Maurer-Cartan equation and perfect complexes

Abstract: It is well-know that a perfect complex on a general ringed spaces, unlike the case on algebraic varieties, is not always strictly perfect, which makes it difficult to investigate perfect complexes by algebraic or analytic methods. The strategy to solve the problem is to take higher structures into account and in this talk we will discuss two approaches to study perfect complexes, one is via twisted complexes and the other is via cohesive modules. Surprisingly the higher structures in both approaches, which have different nature, satisfy the same Maurer-Cartan equation. We will also discuss some applications of these constructions to the study of perfect complexes.