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SUMMARY:Ana Chavez Caliz (Pennsylvania State University)
DTSTART:20220106T161500Z
DTEND:20220106T170000Z
DTSTAMP:20260422T070226Z
UID:CJCS/50
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/50/">Pr
 ojective self-dual polygons</a>\nby Ana Chavez Caliz (Pennsylvania State U
 niversity) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst
 ract\nIn his book "Arnold's Problems\," Vladimir Arnold shares a collectio
 n of questions without answers formulated during seminars in Moscow and Pa
 ris for over 40 years. One of these problems\, stated in 1994\, goes as fo
 llows:\nFind all projective curves projectively equivalent to their duals.
  The answer seems to be unknown even in RP^2.\n\nMotivated by this questio
 n\, in their paper "Self-dual polygons and self-dual curves" from 2009\, D
 . Fuchs and S. Tabachnikov explore a discrete version of Arnold's question
  in 2-dimensions. If P is an n-gon with vertices A_1\, A_3\, ... A_{2n-1}\
 , then its dual polygon P* has vertices B*_2\, B*_4\, ... B*_{2n}\, where 
 B*_i is the line connecting the points A_{i-1}\, A_{i+1}. Given an integer
  m\, a polygon P is m-self-dual if there is a projective transformation f 
 such that f(A_i) = B_{i+m}. \n\nIn this talk\, I will discuss how we can g
 eneralize Fuchs and Tabachnikov's work to polygons in higher dimensions. I
  will include some conjectures which are supported by computational result
 s.\n
LOCATION:https://researchseminars.org/talk/CJCS/50/
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