Mathematical Conversations

This talk will be an introduction to K.-T. Chen's iterated integrals and to the de Rham theory of homotopy groups. I will give an historical introduction, starting with works of Frank Adams (1956) and John Stallings (1975) that have been lost in the sands of time. I'll also indicate how iterated integrals can be used to put mixed Hodge structures on homotopy groups.