Schreiber Differential cohomology is Cohesive homotopy theory

A talk that I gave:

• Differential cohomology is Cohesive homotopy theory

  talk at Higher Geometric Structures along the Lower Rhine, 19-20 June 2014

  (talk notes: pdf)

on how cohesion is a faithful axiomatization of generalized differential cohomology including differential moduli stack constructions such as that of intermediate Jacobians in higher complex analytic geometry.

Related talks

• Differential generalized cohomology in Cohesive homotopy type theory, talk at Formalization of Mathematics, IHP, Paris, 5-9 May 2014

• Some thoughts on the future of modal homotopy type theory, talk at German Mathematical Societty meeting 2015, Hamburg

Related projects

• differential cohomology in a cohesive topos

  • Synthetic Quantum Field Theory

    • Quantum gauge field theory in Cohesive homotopy type theory

    • Type-semantics for quantization

    • Higher toposes of laws of motion

  • cohomology

    • Principal ∞-bundles – models and general theory

    • Fivebrane structures

    • Cosimplicial C-infinity rings and the de Rham complex of Euclidean space

  • ∞-Chern-Weil theory

    • L-∞ algebra connections

    • Cech cocycles for differential characteristic classes

    • Twisted differential structures

      • Twisted Differential String and Fivebrane Structures

      • The moduli 3-stack of the C-field

  • ∞-Chern-Simons theory

    • A higher stacky perspective on Chern-Simons theory

    • Higher Chern-Weil Derivation of AKSZ Sigma-Models

    • 7d Chern-Simons theory and the 5-brane

    • Extended higher cup-product Chern-Simons theories

  • ∞-Wess-Zumino-Witten theory

    • The brane bouquet

  • Higher geometric prequantum theory

    • Classical field theory via Cohesive homotopy types

    • L-∞ algebras of local observables from higher prequantum bundles

    • Local prequantum field theory

  • Motivic quantization of local prequantum field theory

    • Geometric quantization of symplectic and Poisson manifolds

    • Cohomological quantization of local prequantum boundary field theory