BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alina Vdovina (City College of New York) DTSTART:20231114T143000Z DTEND:20231114T153000Z DTSTAMP:20260423T021034Z UID:MathPic/121 DESCRIPTION:Title: Higher dimensional digraphs from cube complexes and their spectral theor y\nby Alina Vdovina (City College of New York) as part of Mathematical Picture Language Seminar\n\n\nAbstract\nWe define k-dimensional digraphs and initiate a study of their spectral theory. The k-dimensional digraphs can be viewed as generating graphs for small categories called k-graphs. G uided by geometric insight\, we obtain several new series of k-graphs usin g cube complexes covered by Cartesian products of trees\, for k≥2. These k-graphs can not be presented as virtual products\, and constitute novel models of such small categories. The constructions yield rank-k Cuntz-Krie ger algebras for all k≥2. We introduce Ramanujan k-graphs satisfying opt imal spectral gap property\, and show explicitly how to construct the unde rlying k-digraphs.\n LOCATION:https://researchseminars.org/talk/MathPic/121/ END:VEVENT END:VCALENDAR