University of Chicago
Department of Mathematics

The combinatorics of 1-fold loop spaces is well understood in terms of geometry of Stasheff's polytopes and is extremely useful. The combinatorics of n-fold loop spaces for n>1 is much more mysterious. In my lecture I will show how higher categorical ideas lead to a new recognition principle for n-fold loop spaces which reveals their hiden combinatorics. If time allows me I will tell about higher dimensional analogues of Stasheff's polytopes and corresponding notions of E_n-algebras (including n= \infty).