Projects
THH and Koszul Duality (in preparation)
I show a simple duality statement for THH - the THHs of two Koszul dual E_1 algebras are Spanier-Whitehead dual.
Quasicategories and Transfer (in preparation) Any additive functor from Waldhausen categories is "transfer additive". I use this to provide another proof that the Becker-Gottlieb transfer factors through the A-theory transfer. We work over an arbitrary infinity-topos, and use this to define the classical THH transfer as a Becker-Gottlieb transfer in a particular infinity-topos.
Parameterized ku-modules (Joint with John Lind, in preparation) We describe a geometric way of going from charted 2-vector bundles to parameterized ku-modules. This provides some geometric intuition behind the work of Baas-Dundas-Rognes.
Explicit Fibrant Replacement in Marked Simplicial Sets (in preparation)
Following a suggestion of Clark Barwick, I provide an explicit fibrant replacement for (certain) marked simplicial sets using a double-Ex construction.
Characteristics and Dwyer-Weiss-Williams
More on this later.
Research Interests
For a very detailed account see my research statement . Broadly, I'm interested in homotopy theory, K-theory and related invariants (such as THH and TC) and higher categories. I'm also becoming interested in the more computational aspects of K-theory, those relating to red-shift and the de Rham-Witt complex.