Generalized scissors congruence

My primary research project on generalized scissors congruence.
  1. "Derived zeta-functions." Joint with Jonathan Campbell and Jesse Wolfson, in preparation.
  2. "Tensor products of assemblers," in preparation.
  3. "The annihilator of the Lefschetz motive." arXiv
  4. "On K1 of an assembler," arXiv.
  5. "The K-theory of assemblers." arXiv
  6. "Simplicial polytope complexes and deloopings of K-theory." Homotopy, Homology and Applications, vol 15, 2, p301-330. PDF
  7. "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.
  1. "A recognition principle for small model categories," arXiv
  2. "Model categories with simple homotopy categories." arXiv

Other projects

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