Speaker: John E. Harper (OSU)
Abstract: We will review the basic invariants of topological spaces and use this to motivate the deep connection between simplicial sets and spaces (they have equivalent homotopy theories), use this to introduce some basic ideas of modern homotopy theory (derived categories and derived functors), and then explore the deep connection between simplicial objects and homological algebra. The upshot of the talk will be to explore a unifying notion of homology of algebraic objects, developed by Quillen, as derived abelianzation. In particular, we will describe some connections between homotopy theory in various algebraic (or topological contexts) and more classical areas of homological algebra such as homology of groups and Andre'-Quillen homology of commutative rings.
Note: Pre-candidacy students can sign up for this lecture series by registering for one or two credit hours of Math 6193, Call/Class # 20913 (with Prof H. Moscovici).