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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20241028T113000
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DTEND;TZID=America/Toronto:20241028T123000
URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-roberto-hernandez-palomares
SUMMARY:Algebraic Graph Theory-Roberto Hernández Palomares
CLASS:PUBLIC
DESCRIPTION:TITLE: Quantum graphs\, subfactors and tensor categories\n\nSPE
 AKER:\n Roberto Hernández Palomares\n\nAFFILIATION:\n University of Water
 loo\n\nLOCATION:\n Please contact Sabrina Lato for Zoom link.\n\nABSTRAC
 T: Graphs and their noncommutative analogues are interesting\nobjects of s
 tudy from the perspectives of operator algebras\, quantum\ninformation and
  category theory. In this talk we will introduce\n equivariant graphs wit
 h respect to a quantum symmetry along with\nexamples such as classical gra
 phs\, Cayley graphs of finite groupoids\,\nand their quantum analogues. We
  will also see these graphs can be\nconstructed concretely by modeling a q
 uantum vertex set by an\ninclusion of operator algebras and the quantum ed
 ge set by an\nequivariant endomorphism that is an idempotent with respect 
 to\nconvolution/Schur product. Equipped with this viewpoint and tools from
 \nsubfactor theory\, we will see how to obtain all these idempotents\nusin
 g higher relative commutants and the quantum Fourier transform.\nFinally\,
  we will state a quantum version of Frucht's Theorem\, showing\nthat every
  quasitriangular finite quantum groupoid arises as certain\nautomorphisms 
 of some categorified graph.
DTSTAMP:20260403T083030Z
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