Algebraic GeometryHigher stacks. Equivariant algebraic K-theory and equivariant intersection theory. Homotopical and derived algebraic geometry. Moduli spaces and derived moduli spaces. Deformation Theory. dg-derived categories. Derived non-abelian Hodge theory. Derived motives.
Algebraic TopologyModel categories. Simplicial and Segal categories. Waldhausen K-theory. Geometry over ring spectra. Topological modular forms. Arithmetic aspects of stable homotopy theory.