Schreiber ItaCa Fest 2025

A talk that I will have given:

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• Urs Schreiber$\;\;\;$ on joint work with $\;\;\;$ Hisham Sati:

  
  

  Geometric Orbifold Cohomology

  in Singular-Cohesive $\infty$-Topoi

  slides: [to appear here]

  
  

  

  talk at:

  ItaCa Fest 2025 (17 June 2025)

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Abstract. Addressing exigent questions in quantum materials (and in M-theory) hinges on understanding twisted differential cohomology of orbifolds in extraordinary nonabelian generality. However previous theory has been fragmentary and often ad hoc, lacking a transparent unifying perspective.

I begin by highlighting and illustrating the abstract nature of cohomology as being about maps to classifying spaces, in broad generality. This allows to transparently state the fundamental theorem of twisted generalized orbifold cohomology. Then I explain where this does take place: in singular-cohesive $\infty$-topoi, where a system of adjoint modal operators neatly organizes the subtle nature and intricacies of the subject.

This is an exposition of selected constructions and results from our two monographs-to-appear:
- “Equivariant Principal $\infty$-Bundles” (CUP)
- “Geometric Orbifold Cohomology” (CRC).

Related exposition:

• Higher Topos Theory in Physics

Related talks:

• Higher and Equivariant Bundles

  talk via Feza Gürsey Higher Structures Seminar,

  Feza Gürsey Institute Istanbul, 2022

• Twisted equivariant differential (TED) K-theory via diffeological stacks

  talk at Global Diffeology Seminar, 03 Nov 2022

  slides: pdf