Research

Papers and Preprints

• The motivic fundamental group of the punctured projective line (Journal of K-Theory, 2010)

  We describe a construction of an object associated to the fundamental group of the projective line minus three points in the Bloch-Kriz category of mixed Tate motives. This description involves Massey products of Steinberg symbols in the motivic cohomology of the ground field. This work was part of my 2008 Ph.D. thesis under Peter May at the University of Chicago.

• Strictification of categories weakly enriched in symmetric monoidal categories (Theory and Applications of Categories, 2010)

  We offer two proofs that categories weakly enriched over symmetric monoidal categories can be strictified to categories enriched in permutative categories. This is a "many 0-cells" version of the strictification of bimonoidal categories to strict ones.

• Enriched model categories and diagram categories (Joint with J. P. May, submitted, available on the ArXiv)

  We study enriched model categories. One of the main questions is when one can replace a given V-model cateogry by a category of presheaves with values in V. We use this to gain a better understanding of equivariant homotopy theory.

• Models of G-spectra as presheaves of spectra (Joint with J. P. May, submitted, available on the ArXiv)

  This works specializes the above theory to the case of equivariant spectra. Restricting to the case of a finite group, we give a good working model for G-spectra which is built out of finite G-sets and nonequivariant spectra.

• Chaotic categories and equivariant classifying spaces (Joint with J. P. May and M. Merling, available on the ArXiv)

  We give simple and precise models of equivariant classifying spaces. We need these models for the paper below on equivariant infinite loop space theory, but the models are of independent interest in equivariant bundle theory.

• Permutative G-categories and equivariant infinite loop space theory (Joint with J. P. May, in progress)

  This article supplies much of the results from equivariant infinite loop space theory that are needed in our paper on G-spectra. The equivariant Barratt-Priddy-Quillen theorem is one of the central results, and we rederive the tom Dieck splitting of the fixed points of equivariant suspension spectra from a category-level decomposition.

• On operads and Taylor towers (Joint with R. McCarthy, in progress)

  We consider splitting questions in the calculus of functors.