I am a mathematics PhD student at Princeton University (expected 2018) with a focus on Voevodsky's theory of motives and its connections and applications to stable homotopy theory, birational geometry, and arithmetic. Recently, I have been thinking about

  • Integration of Voevodsky motives, motives of K-equivalent varieties, and connections to the existence of motivic t-structures;
  • Triangulated categories of mixed motives and l-independence;
  • Derived motivic measures; and
  • (Stable) motivic homotopy theory and its connections to classical and etale homotopy theory.

Papers and Preprints.

1. Comparison of Stable Homotopy Categories and a Generalized Suslin-Voevodsky Theorem. Submitted. PDF
-You can find in this paper a proof that the constant sheaf functor induces, after inverting p, a fully faithful functor from the classical stable homotopy category to the motivic stable homotopy category over an algebriacally closed field of characteristic exponent p. Additionally, there is a proof of a homotopy-theoretic generalization of the Suslin-Voevodsky comparison theorem.
2. Integration of Voevodsky motives. Preprint. PDF
-I develop a theory of integration for Voevodsky motives, and show that it circumvents some of the complications of motivic integration. Using this, I deduce new arithmetic and geometric information about K-equivalent varieties over fields. Finally, I show that if there is a motivic t-structure on the category of rational geometric Voevodsky motives, then K-equivalent varieties have the same rational motives.
3. A Universal Derived Motivic Measure. In preparation. Joint with Adeel Khan.