Morse homology via the stack of broken linesMPIM

by Qingyuan Bai (MPIM)

Thursday Dec 11, 2025, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

The Morse chain complex gives an elementary way to compute singular homology groups of a closed manifold, by means of counting numbers. I will explain this beautiful construction along with some basic examples. I will then motivate the work of Lurie-Tanaka, which aims to perform a similar construction in the context of stable homotopy theory where the notion of counting becomes more intricate. If I have time, I will mention some possible applications of these ideas in other disciplines of mathematics.

The main part of this talk will only assume knowledge of calculus and linear algebra, but the final part might need much more (mostly curiosities and imaginations).