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DTSTART;TZID=America/Toronto:20250310T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-joseph-w-iverson
SUMMARY:Algebraic Graph Theory-Joseph W. Iverson
CLASS:PUBLIC
DESCRIPTION:TITLE: Covers of the complete graph\, equiangular lines\, and 
 the\nabsolute bound\n\nSPEAKER:\n Joseph W. Iverson\n\nAFFILIATION:\n Iowa
  State University\n\nLOCATION:\n Please contact Sabrina Lato for Zoom li
 nk.\n\nABSTRACT: We discuss equiangular lines and covers of the complete\n
 graph. The relationship between these objects dates to at least 1992\,\nwh
 en Godsil and Hensel showed that any distance-regular antipodal\ncover of 
 the complete graph (DRACKN) produces an ensemble of\nequi-isoclinic subspa
 ces. In the case of a regular abelian DRACKN\,\nthis produces equiangular 
 lines.\nIn the first part of the talk\, we combine Godsil and Hensel's the
 orem\nwith a 2017 observation of Waldron to explain why (with a single\nex
 ception) there DO NOT exist regular abelian DRACKNs that would\ncreate d^2
  equiangular lines in d-dimensional complex space\, to\nachieve Gerzon's \
 "absolute bound\". This rules out a family of\notherwise feasible DRACKN p
 arameters that were enunciated in a 2016\npaper of Coutinho\, Godsil\, Shi
 razi\, and Zhan.\nIn the second part of the talk\, we introduce \"roux\"\,
  a slight\ngeneralization of regular abelian DRACKNs. Roux are covers of t
 he\ncomplete graph that produce equiangular lines. They come up naturally\
 nin the classification of doubly transitive lines\, all of which arise\nfr
 om roux. Keeping hope alive for the present\, we enunciate an\ninfinite fa
 mily of feasible roux parameters that would produce\nequiangular lines ach
 ieving Gerzon's absolute bound.\nBased on joint work with Dustin Mixon.
DTSTAMP:20260403T082840Z
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