# Floris van Doorn: Towards Spectral Sequences for Homology

**Time: **
Wed 2018-09-19 10.00 - 11.45

**Lecturer: **
Floris van Doorn (Carnegie Mellon University)

**Location: ** Room 31, building 5 kräftriket, Department of Mathematics, Stockholm University ￼

Abstract: Homotopy type theory has lead to a new research area, synthetic homotopy theory, in which results in homotopy theory are stated and proven in type theory. Many advances have been made in doing cohomology theory in homotopy type theory, such as the Mayer–Vietoris sequence and the Serre and Atiyah–Hirzebruch spectral sequences for cohomology.

The progress in homology theory is much slower. During this talk I will explain some difficulties in doing homology theory and talk about the work in progress to get the Serre and Atiyah–Hirzebruch spectral sequences for homology. Along the way, I will discuss the related project of the coherent associativity of the smash product. Some basic knowledge of homotopy type theory is assumed for this talk.