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Center for Nonlinear Studies |
Cihan Okay is an Assistant Professor of Mathematics at Bilkent University in Ankara. Before that, he was a postdoctoral fellow at the Stewart Blusson Quantum Matter Institute at the University of British Columbia (UBC) and worked in the research group of Robert Raussendorf (2017-2020). He obtained his PhD in mathematics (algebraic topology) at UBC under the supervision of Alejandro Adem (2014). He spent three years (2014-2017) at Western University as a postdoctoral fellow under the supervision of Rick Jardine.
In modern homotopy theory, spaces are represented by combinatorial models called simplicial sets. Their elegant formulation gives them great expressive power to capture spaces up to homotopy. Simplicial distributions are basic mathematical objects that mix simplicial sets with probabilities. That is, they model probability distributions on spaces. In my talk, I will show how simplicial distributions provide a framework for studying a central quantum feature associated with probabilities, known as contextuality. A typical measurement scenario consists of a set of measurements and outcomes, whereas simplicial distributions can be defined for spaces of measurements and outcomes. Our approach unifies and goes beyond two earlier approaches: the sheaf-theoretic (Abramsky-Brandenburger) and group cohomological (Okay-Roberts-Bartlett-Raussendorf).
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Host: Yigit Subasi (CCS-3)