Multiplicative structures on homotopy spectral sequences I

This mostly expository paper records some basic facts about towers of homotopy fiber sequences. We give a proof that a pairing of towers induces a pairing of associated spectral sequences, for towers of spaces and towers of spectra

A curious example of two model categories and some associated differential graded algebras

The paper gives a new proof that the model categories of stable modules for the rings Z/(p^2) and (Z/p)[\epsilon]/(\epsilon^2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an example of two differential graded algebras which are derived equivalent but whose associated model categories of modules are not Quillen equivalent. As a bonus, we also obtain derived equivalent dgas with non-isomorphic K-theories

Enriched model categories and an application to additive endomorphism spectra

We define the notion of an additive model category, and we prove that any additive, stable, combinatorial model category has a natural enrichment over symmetric spectra based on simplicial abelian groups. As a consequence, every object in such a model category has a naturally associated endomorphism ring inside this spectra category. We establish the basic properties of this enrichment. We also develop some enriched model category theory. In particular, we have a notion of an adjoint pair of functors being a 'module' over another such pair. Such things are called "adjoint modules". We develop the general theory of these, and use them to prove a result about transporting enrichments over one symmetric monoidal model category to a Quillen equivalent one.Comment: Sections completely re-organized from previous version. Mathematical content all the sam

CURRENT PROGRAMS FOR MEETING SPECIAL EDUCATION AND TRAINING NEEDS - A REPORT

Teaching/Communication/Extension/Profession,

S=0 pseudoscalar meson photoproduction from the proton

Many measurements of pseudoscalar mesons with S = 0 photoproduced on the proton have been made recently. These new data are particularly useful in theoretical investigations of nucleon resonances. How the new data from various labs complement each other and help fill in the gaps in the world data set is disscussed, with a glance at measurements to be made in the near future. Some theoretical techniques used to explain the data are briefly described.Comment: 6 pages, 3 figures, Nstar workshop proceeding to be published with World Scientifi