Bashar Saleh: Weights in homotopy theory

Abstract.

Weight decompositions on algebraic models for spaces serve as a tool for deriving formality, p-universality, the existence of derationalizations, and other homotopical properties. In the first part of the talk, I will present different types of weight decompositions and discuss the homotopical consequences of each type.

In the second part of the talk, I will present recent joint work with J. Cirici that results in restrictions on the rational homotopy types of certain mapping spaces and the classifying spaces of homotopy automorphisms, achieved through the theory of positive weight decompositions.