Equivariant contextuality

Abstract: Simplicial quantum contextuality, introduced by Okay, Kharoof and Ipek, is a framework for using topological methods based on simplicial sets to study quantum contextuality. It subsumes earlier approaches - topological (Okay, Roberts, Bartlett, Raussendorf) and sheaf-theoretic (Abramsky, Brandenburger).

In this talk we will discuss how group action can be composed into this framework. To this end, we will use such tools as Borel construction and partial groups in the sense of Broto-Gonzalez. We will start with the notions of equivariant simplicial distributions and equivariant contextuality and connect them with the Borel construction. Then we will proceed with the cohomological aspects, which are based on the extensions of partial groups and cofibre sequences of simplicial sets.

The talk is based on a joint work with Cihan Okay, to appear on arxiv soon.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos