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DTSTART;TZID=America/Toronto:20250826T160000
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URL:https://uwaterloo.ca/pure-mathematics/events/analysis-seminar-200
SUMMARY:Analysis Seminar
CLASS:PUBLIC
DESCRIPTION:BEATRICE-HELEN VRITSIOU\, UNIVERSITY OF ALBERTA\n\n_On the Hadw
 iger-Boltyanski illumination conjecture for convex bodies\nwith many symme
 tries _\n\nLet us think of a convex body in R^n (convex\, compact set\, wi
 th\nnon-empty interior) as an opaque object\, and let us place point light
 \nsources around it\, wherever we want\, to illuminate its entire surface.
 \nWhat is the minimum number of light sources that we need? The\nHadwiger-
 Boltyanski illumination conjecture from 1960 states that we\nneed at most 
 as many light sources as for the n-dimensional hypercube\,\nand more gener
 ally\, as for n-dimensional parallelotopes. For the\nlatter their illumina
 tion number is exactly 2^n\, and they are\nconjectured to be the only equa
 lity cases.\n\nThe conjecture is still open in dimension 3 and above\, and
  has only\nbeen fully settled for certain classes of convex bodies (e.g. z
 onoids\,\nbodies of constant width\, etc.). In this talk I will briefly di
 scuss\nsome of its history\, and then focus on recent progress towards\nve
 rifying the conjecture for all 1-symmetric convex bodies and certain\ncase
 s of 1-unconditional bodies.\n\nMC 5501
DTSTAMP:20260502T041555Z
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