Schedule of talks:

Abstracts

(Joshua second Talk): There are certain other operations, distinct from the cohomology operations introduced by Voevodsky in motivic (and etale) cohomology with finite coefficients. These behave differently with respect to weights and are often called classical or simplicial operations. The talk will discuss the precise relationship between these operations and the motivic operations of Voevodsky. We will also look briefly at the source of the classical operations, which is a certain coherently homotopy commutative and associative ring structure on the motivic complex and consider some applications of this structure.

(Harper Talk I): An important theme in current work in homotopy theory is the investigation and exploitation of enriched algebraic structures on spectra that naturally arise, for instance, in algebraic topology, algebraic K-theory, and derived algebraic geometry. Such structured ring spectra or ``geometric rings'' are most simply viewed as algebraic-topological generalizations of the notion of ring from algebra and algebraic geometry. This talk will describe recent progress, in joint work with M. Ching, on an analog of Quillen--Sullivan theory for structured ring spectra.

(Harper Talk II): This talk will outline and motivate a proof for establishing a homotopic descent type result for the topological Quillen homology of structured ring spectra. A new intermediate result of independent interest, is higher homotopy excision for structured ring spectra, analogous to Goodwillie's higher homotopy excision results for spaces. This is joint work with Michael Ching.

(Ogle Talk I): We discuss the original question posed by Milnor in his paper "Algebraic K-theory and Quadratic Forms" (Inv., 1970). This first talk will be background, covering very classical material: K_1, K_2, Steinberg symbols and the K-theory product, Milnor K-theory, and the partial results proved by Milnor in the very early days of Algebraic K-theory. The objective is to show how efforts to answer this question lead to the work of Voevodsky and others, which ultimately led to Voevodsky's solution of the conjecture.

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