Alexander Berglund: Algebraic models in topology

Algebraic invariants, such as the Euler characteristic, Betti numbers, cohomology and homotopy groups, are tools for obtaining qualitative information about topological spaces. In particular, such tools are of fundamental importance in the classification of manifolds. The idea of an algebraic model is to endow the invariants with additional structure, yielding a complete invariant of the homotopy type in favorable situations.

In this talk, I will give an introduction to these ideas through the example of de Rham cohomology. Towards the end of the talk, I will briefly indicate connections to my own research.