We show that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of l-adic étale cobordism over an algebraically closed field of positive characteristic. This implies that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of Atiyah and Hirzebruch for non-algebraic integral cohomology classes and of Totaro for non-trivial elements in the Griffiths group also work in positive characteristic.

In this talk, we will explore some properties of Chern classes. In the axiomatic way, these properties uniquely determine these Chern classes.

In this talk I will explain how the solution of the wave equation can be used to explain music scales, temperament (i.e., music tuning) and harmony. We will also do a few experiments on a guitar.

The (stable) chromatic spectral sequence has had a significant impact on our understanding of the stable homotopy groups of the spheres. I will talk about preliminary attempts to construct an unstable version. I will try to describe a filtration of the stable chromatic spectral sequence induced by the Hopf rings for the odd spheres. There are natural questions that arise in the unstable world (e.g. an unstable version of the Morava stabilizer algebra) and a chromatic interpretation of the Hopf invariant.

Normal forms have been used since Poincare. The problem of converting an element in a Lie algebra into its normal form can be a difficult calculation. In joint work with Rick Churchill we have applied the method of spectral sequences to this problem. The talk will be both an introduction to normal forms and (to a lesser degree) an introduction to spectral sequences.

There is some interest in the structure of toric spaces (e.g. moment angle complexes, toric manifolds, subspace arrangements, etc.) In recent work with Tony Bahri, Fred Cohen and Sam Gitler we have shown that many of these spaces stably split into canonical pieces. I shall describe how this splitting determines the product structure in the cohomology of a generalized moment angle complex and allows us to compute the KO theory of Davis-Januskiewicz spaces (joint with BBCG, Don Davis and Nigel Ray).

TBA

In this talk I will explain how the celebrated theorem of Borel-Weil-Bott provides a natural realization of some extreme components of the tensor product of two irreducible modules of simple algebraic groups. I will also discuss a number of connections of our construction with problems coming from Representation Theory, Combinatorics, and Geometry, including questions about the Littlewood-Richardson cone related to Horn's conjecture, settled by Knutson and Tao in the late 1990's.

The talk is based on joint work with Mike Roth.