Research

I work in Algebraic geometry, Number theory, and Homological Algebra. I study the p-adic Hodge theory, motives and algebraic K-theory. I'm interested in applications of homotopy-theoretic methods to Algebra. Here you can find a review of some of my papers. The actual texts are below. Also here is a description of my current research.

• On the center of the ring of differential operators on a smooth variety over Z/p^nZ (2011). pdf
  (with Allen Stewart).

• Some remarks on the integral Hodge realization of Voevodsky's motives (2011). pdf
  

• Motivic integral of K3 surfaces over a non-archimedean field (2011). pdf
  (with Allen Stewart).

• On the derived DG functors (2010). pdf
  

• Integrality theorems in the theory of topological strings (2009). pdf
  (with Albert Schwarz).

• The Albanese functor commutes with the Hodge realization (2008). pdf
  

• On the N-integrality of instanton numbers (2008). pdf
  

• A DG guide to Voevodsky's motives (2008). pdf
  (with Alexander Beilinson).
  

• Nonabelian Hodge Theory in Characteristic p (2007). pdf
  (with Arthur Ogus).
  

• Frobenius transformation, mirror map and instanton numbers (2006). pdf
  (with Albert Schwarz).
  

• Integrality of the instanton numbers and p-adic B-model (2006). pdf
  (with Maxim Kontsevich and Albert Schwarz).
  

• Non-commutative compactifications and elliptic curves (2003). pdf
  (with Yan Soibelman).
  

• Hodge structure on the fundamental group and its application to p-adic integration (2003). pdf
  

• $\gamma$-functions of representations and lifting (2000). pdf
  (Author of an appendix.)

• On measure of K-points of an abelian variety, where K is a local field (2000). pdf