Preprints

The following three preprints are based on my thesis.

Differentiabel sheaves I: Fractured ∞-toposes and compactness (submitted)

Differentiabel sheaves II: Local contractibility and cofinality

Differentiabel sheaves III: Homotopical calculi and the smooth Oka principle

Theses

PhD thesis: A convenient category for geometric topology

I study the shape theory of the ∞-topos of differentiable stacks in great detail. In the process I recover Cisinski's model structure on the ordinary category set valued sheaves on smooth manifolds, yielding a model for homotopy types. This category has excellent formal properties, making it an excellent replacement for the category of topological spaces in applications to geometric topology.

A future version will have more detailed proofs, and contain a new construction of the model structure on topological spaces, as well as a new proof that the geometric realisation-total singular complex functor is a Quillen equivalence.

Master thesis: Pro-algebraic resolutions of regular schemes

For any regular scheme over an algebraically closed field of characteristic 0 I construct a resolution by commutative pro-algebraic groups, following an idea outlined by Serre in a letter to Grothendieck.