Date: 1 March 2013, 4:30pm Location: Hempfield High School, Room 213 Speaker: Thomas Tradler, City University of New York Title: Holonomy via higher Hochschild complexes Abstract. We will recall the notion of simplicial sets and simplicial spaces in specific elementary examples, and show how this naturally produces the Hochschild complex of an associative algebra and higher analogues of it. We will use the Chen iterated integral map to derive the holonomy of a vector bundle purely from connection data encoded in a Hochschild complex. Going one level higher, a similar construction also encodes the holonomy of a gerbe via data living on a torus Hochschild complex.