Effective constructions in algebraic topology and applications

https://zoom.us/j/93172910947
Meeting ID: 931 7291 0947
For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

There is some tension between functoriality and constructibility in algebraic topology reaching back to its origins. For example, the cohomology of a space X could be described in terms of homotopy classes of maps from X to certain spaces, or via a cochain complex generated by a combinatorial representation of X. In this survey talk we will discuss effective constructions of finer structure enhancing the cohomology of X in combinatorial terms. This so called E-infinity structure and associated cochain level operations on X, have become important for new applications of cohomology in the study of, for example, topological QFTs and persistent homology.