A great challenge in homotopy theory is determining properties of the homotopy groups of finite simply-connected CW-complexes. One approach is to try to decompose the based loops on such a space into a product of more recognizable factors. In these talks we will investigate a new loop space decomposition method that applies to many interesting families of spaces, with special focus on various classes of Poincaré Duality complexes. Among the consequences are resolutions of instances of famous conjectures: by Moore on the relation between the torsion and rational homotopy groups, and by Gromov and Vigué-Poirrier on exponential growth in the rational homology of free loop spaces.

You can download lecture materials(board writings) of 1st – 5th lectures from Resources(10).