Speaker: John E. Harper (OSU)
Abstract: We will introduce the homotopy theoretic notion of commutative rings, called structured ring spectra, which makes precise the notion of "doing commutative algebra over the spheres". In this context, the commutative ring spectrum S, equal to the collection of spheres S^n as n ranges over the non-negative integers, plays the role of the ring of integers. One can then "do commutative algebra over S". We will review the basic invariants of such homotopy theoretic rings and the corresponding notion of topological Quillen homology. The upshot of the talk will be to understand some recent results about how much of a homotopy theoretic ring can be recovered from its topological Quillen homology; in particular, we will prove an analog, in the context of structured ring spectra, of Serre's classical finiteness theorem for topological spaces.
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).
