We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …

The concept of orbifolds should unify differential geometry with equivariant homotopy theory,
so that orbifold cohomology should unify differential cohomology with proper equivariant …

On one hand, together with Pelle Steffens, we recently characterized the infinity category of
derived manifolds up to equivalence by a universal property. On the other hand, it is shown …

This work is the first in a series laying the foundations of derived geometry in the $ C^{\infty}
$ setting, and providing tools for the construction and study of moduli spaces of solutions of …

If X is a manifold then the R-algebra C∞(X) of smooth functions c: X→ R is a C∞-ring. That
is, for each smooth function f: Rn→ R there is an n-fold operation Φf: C∞(X) n→ C∞(X) …

We give an exposition of graded and microformal geometry, and the language of Q‐
manifolds. Q‐manifolds are supermanifolds endowed with an odd vector field of square …

We develop the theory of derived differential geometry in terms of bundles of curved $
L_\infty [1] $-algebras, ie dg manifolds of positive amplitudes. We prove the category of …

Shulman's spatial type theory internalizes the modalities of Lawvere's axiomatic cohesion in
a homotopy type theory, enabling many of the constructions from Schreiber's modal …

We prove that dg manifolds of finite positive amplitude, that is, bundles of positively graded
curved-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a …

The key open problem of string theory remains its non‐perturbative completion to M‐theory.
A decisive hint to its inner workings comes from numerous appearances of higher structures …