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UID:23d4a3c242e1ac9215ef76269bcc5f1c
CATEGORIES:Mathematical Physics Seminar
CREATED:20250430T103816
SUMMARY:Webinar: Camillo De Lellis - Besicovitch's 1/2 problem and linear programming 
LOCATION:Zoom
DESCRIPTION:Camillo De Lellis – Institute for Advanced Study\n \nWednesday, May 21st, 2
 025\nZoom opens: 10:30AM DST\nSeminar Begins: 10:45AM DST\n \nBesicovitch's
  1/2 problem and linear programming\nIn 1928 Besicovitch formulated the fol
 lowing conjecture. Let E be a 1-dimensional set of the plane. The set E can
 not be a fractal if at all sufficiently small scale around (almost all) its
  points the length of the set in a disk is slightly more than half of the d
 iameter of the disk. It was proved by Dickinson that the threshold cannot b
 e lowered, while Besicovitch himself showed first that the statement holds 
 if the thresold is slightly smaller than 1, and improved it in 1938 to 3/4.
  Since then his bound was improved only once by Preiss and Tiser in the nin
 eties to an (algebraic) number which is approximately 0.735. In this talk I
  will report on further progress stemming from a joint work with Federico G
 laudo, Annalisa Massaccesi, and Davide Vittone. Besides improving the bound
  of Preiss and Tiser to a substantially lower number, our work proposes a f
 amily of variational methods to find and improve the latter bound. We can i
 mprove Preiss and Tiser bounds both with a pen-and-paper proof and with the
  assistance of a computer (which is used to examine a very large, but finit
 e, number of cases). The latter is in fact a feasible computation because a
  part of the variational problems can be formulated as a linear programming
  task.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="text-align: center;"><strong>Camillo De Lellis – Institute for Ad
 vanced Study</strong></p><p style="text-align: center;"><strong>&nbsp;</str
 ong></p><p style="text-align: center;"><strong>Wednesday,&nbsp;May 21st,&nb
 sp;2025</strong></p><p style="text-align: center;"><strong>Zoom opens: 10:3
 0AM DST</strong></p><p style="text-align: center;"><strong>Seminar Begins:&
 nbsp;10:45AM DST</strong></p><p style="text-align: center;"><strong>&nbsp;<
 /strong></p><p style="text-align: center;"><strong>Besicovitch's 1/2 proble
 m and linear programming</strong></p><p>In 1928 Besicovitch formulated the 
 following conjecture. Let E be a 1-dimensional set of the plane. The set E 
 cannot be a fractal if at all sufficiently small scale around (almost all) 
 its points the length of the set in a disk is slightly more than half of th
 e diameter of the disk. It was proved by Dickinson that the threshold canno
 t be lowered, while Besicovitch himself showed first that the statement hol
 ds if the thresold is slightly smaller than 1, and improved it in 1938 to 3
 /4. Since then his bound was improved only once by Preiss and Tiser in the 
 nineties to an (algebraic) number which is approximately 0.735. In this tal
 k I will report on further progress stemming from a joint work with Federic
 o Glaudo, Annalisa Massaccesi, and Davide Vittone. Besides improving the bo
 und of Preiss and Tiser to a substantially lower number, our work proposes 
 a family of variational methods to find and improve the latter bound. We ca
 n improve Preiss and Tiser bounds both with a pen-and-paper proof and with 
 the assistance of a computer (which is used to examine a very large, but fi
 nite, number of cases). The latter is in fact a feasible computation becaus
 e a part of the variational problems can be formulated as a linear programm
 ing task.</p>
CONTACT:Camillo De Lellis
DTSTAMP:20260828T085946
DTSTART;TZID=America/New_York:20250521T104500
DTEND;TZID=America/New_York:20250521T120000
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