Abstract: The theory of Lie groups originated from Sophus Lie's work on symmetry groups of differential equations. Those are transformation groups acting on the space of independent and dependent variables of a differential equation, which transform a solution to another solution.

Our focus is on 1-parameter connected Lie groups and we use the generating vector field as a powerful tool for the calculations. Once we obtain a symmetry group for a differential equation, we are able to construct new solutions from already known ones.

Abstract: We will use (primary and) secondary cohomology operations to describe the structure of the stable stems in low dimensions and compute a few Toda brackets in the stable stems.

Abstract: I will give a general introduction to the subject of Massey products and Toda brackets, suitable for a general mathematical audience. I will describe some of their many uses in algebra and topology, and I will present some new results about the general theory of fourfold Massey products.