Schreiber
Differential generalized cohomology in Cohesive homotopy type theory

A talk that I once gave:

---

• Urs Schreiber

  Differential generalized cohomology in Cohesive homotopy type theory

  (pdf notes)

  talk at

  IHP trimester on Semantics of proofs and certified mathematics

  Workshop 1: Formalization of Mathematics,

  Institut Henri Poincaré,

  Paris, 5-9 May 2014

on the differential cohomology hexagon in cohesive homotopy type theory and some comments on the application to Synthetic Quantum Field Theory.

---

Related talks

• Differential cohomology is Cohesive homotopy theory, talk at Higher Geometric Structures along the Lower Rhine June 2014, 19-20 June 2014

• Some thoughts on the future of modal homotopy type theory, talk at German Mathematical Society 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