# Research

### Generalized scissors congruence

My primary research project on generalized scissors congruence.
- "Derived zeta-functions." Joint with Jonathan Campbell and Jesse Wolfson,
in preparation.
- "Tensor products of assemblers," in preparation.
- "The annihilator of the Lefschetz
motive." arXiv
- "On K
_{1} of an assembler," arXiv.
- "The K-theory of assemblers." arXiv
- "Simplicial polytope complexes and deloopings of K-theory."
*Homotopy, Homology and Applications*, vol 15, 2, p301-330. PDF
- "Scissors congruence as K-theory."
*Homotopy, Homology and Applications*, vol 14, 1, p181-202. PDF

My thesis, written under the supervision of Michael Hopkins,
is here.
### Classification of model categories

This is a joint project with Jean-Marie Droz. The goal of this project is to
classify model category structures and answer the question of when a relative
category is associated to a model category.
- "A recognition principle for small model categories," arXiv
- "Model categories with simple homotopy categories." arXiv

### Other projects

- "Homotopy theory through posets." Joint with Peter May and Marc Stephan, in preparation.
- "Principal ideals in mod-l Milnor K-theory" Joint with Charles
Weibel. arXiv.
- "The category of Waldhausen categories as a closed multicategory." arXiv
- "On the higher topological Hochschild homology of
**F**_{p} and
commutative **F**_{p}-group algebras." Joint with Irina Bobkova,
Ayelet Lindenstrauss, Kate Poirier, Birgit Richter. arXiv
- "A generalization of Wigner's Law."
*Comm. Math. Phys.*, vol 268, 2,
p.403-414. here