BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Davey Fitzpatrick (Princeton University) DTSTART:20200507T190000Z DTEND:20200507T200000Z DTSTAMP:20260422T212746Z UID:URocCombinatorics/1 DESCRIPTION:Title: Distance problems for planar hypercomplex numbers\nby Davey Fitzpatrick (Princeton University) as part of University of Rochester comb inatorics seminar\n\nLecture held in Zoom MeetingID797681224.\n\nAbstract\ nIn this talk\, I will discuss the unit distance and distinct distances pr oblems over the planar hypercomplex numbers: the dual numbers D and the do uble numbers S. I will show that the distinct distances problem in S^2 beh aves similarly to the original problem in R^2. The other three problems be have rather differently from their real analogs. We can study those three problems by introducing various notions of the multiplicity of a point set . The analysis is based on an understanding of the geometry of the dual pl ane and of the double plane. We will also rely on classical results from d iscrete geometry\, such as the Szemerédi-Trotter theorem.”\n LOCATION:https://researchseminars.org/talk/URocCombinatorics/1/ END:VEVENT END:VCALENDAR