Schreiber What, and for what is Higher geometric quantization

A series of talks that I have given:

• What, and for what is Higher geometric quantization?

  at Workshop on Higher Gauge Theory and Higher Quantization, Edinburgh, 25-26 June 2014

  and at Symmetries and correspondences in number theory, geometry, algebra, physics: intra-disciplinary trends, Oxford, July 5-8 2014

  (pdf talk notes)

on higher geometric quantization. Details on the first part of the story are in

• Classical field theory via Cohesive homotopy types (pdf)

and on the second part of the story in

• Quantization via Linear homotopy types

For more exposition see

• Higher Structures in Mathematics and Physics

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