I am interested in abstract homotopy theory and its applications to geometry, especially the geometry of structured ring spectra, both commutative (derived algebraic geometry) and associative (noncommutative algebraic geometry). In particular, my current research is focused on:
- motivic homotopy theory of derived schemes
- algebraic cycles on derived schemes
- saturated dg-categories
- algebraic K-theory of stable ∞-categories
The following expository note explains some folklore results about derived categories of varieties, and a conceptual proof of a theorem of D. Orlov.