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DTSTART:20230312T070000
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DTSTART;TZID=America/Toronto:20240212T113000
SEQUENCE:0
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DTEND;TZID=America/Toronto:20240212T123000
URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-maxwell-levit
SUMMARY:Algebraic Graph Theory - Maxwell Levit
CLASS:PUBLIC
DESCRIPTION:TITLE: Subconstituents of Drackns \n\nSPEAKER:\n Maxwell Levit
 \n\nAFFILIATION:\n Simon Fraser University\n\nLOCATION:\n Please contact 
 Sabrina Lato for Zoom link.\n\nABSTRACT: For a distance-regular graph X a
 nd an arbitrary vertex v\, we\noften find interesting structure in the sub
 graph of X induced on\nvertices at distance 2 from v. \n\nFor example:\n\n
 Any strongly-regular graph with parameters (n\,k\,a\,k/2) can be found at\
 ndistance 2 from a vertex in a distance-regular graph of diameter 3.\n\nCe
 rtain distance-regular graphs of diameter 3 can be found at distance\n2 fr
 om a vertex in a Moore graph of girth 5.\n\nThese (and more) examples are 
 known as second-subconstituents\, and\nthey can be studied using the Terwi
 lliger (or subconstituent) algebra\nof X. I will discuss this theory in th
 e case that X is a\ndistance-regular antipodal cover of a complete graph (
 drackn). This\nsetting generalizes the first example and includes the seco
 nd.\n\nI will describe some general techniques for studying the Terwillige
 r\nalgebras of drackns and then restrict to drackns without triangles. In\
 nthis setting I will explain how to compute the spectrum of the\nsecond-su
 bconstituent of any triangle-free drackn\, except possibly the\nsecond-sub
 constituent OF a second-subconstituent of a Moore graph of\nvalency 57.
DTSTAMP:20260404T054718Z
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