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Texas A&M University
Mathematics

Events for 09/30/2019 from all calendars

Michael Brannan Promotion Talk

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Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Michael Brannan Promotion Talk, Texas A&M University

Description:

TITLE: Graphs, non-local games, and quantum symmetry groups.

ABSTRACT: A well-known theorem of Lov\'asz says that two finite graphs X and Y are isomorphic if and only if for each graph H, the number of graph homomorphisms from H to X equals the number of graph homomorphisms from H to Y. In this talk, we will consider the following question: What happens if we only ask that the number of homomorphisms from H to X and the number of homomorphisms from H to Y be equal for planar graphs H? I will explain how this planar relaxation of graph isomorphism admits two remarkably different interpretations in terms of (1) the theory of non-local games from quantum information theory, and (2) the algebraic notion of a quantum symmetry group of a graph. I will explain how these two very different perspectives on the same idea can be exploited to construct graphs whose quantum symmetry groups have interesting operator algebraic properties.
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