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BEGIN:VEVENT
UID:www.tcs.tifr.res.in/event/1449
DTSTAMP:20240710T110123Z
SUMMARY:Sperner's lemma and the equidissection of regular polygons
DESCRIPTION:Speaker: Pranshu Gaba (TIFR)\n\nAbstract: \nEquidissection of a
  regular polygon is the problem of dissecting the polygon into triangles o
 f equal area. Given a regular n-gon and a positive integer m\, we ask if i
 t is possible to equidissect the n-gon into m triangles. To answer this qu
 estion\, we make use of Sperner's lemma along with some elementary number 
 theory. Sperner's lemma is a major combinatorial result that has found app
 lications in topics such as fixed-point computation and fair division.We s
 hall see Sperner's lemma and its proof\, and use it to solve the equidisse
 ction problem for regular polygons. We will also look at some polygons tha
 t cannot be equidissected into m triangles for any positive m. Finally\, w
 e will go over the equidissection problem for higher-dimensional hypercube
 s.References:- Monsky\, P. (1970). On Dividing A Square Into Triangles. Th
 e American Mathematical Monthly\, 77(2)\, 161–164. https://doi.org/10.1
 080/00029890.1970.11992441- Stein\, S. (2004). Cutting a Polygon into Tria
 ngles of Equal Areas. The Mathematical Intelligencer 26\, 17–21. https:
 //doi.org/10.1007/BF02985395\n
URL:https://www.tcs.tifr.res.in/web/events/1449
DTSTART;TZID=Asia/Kolkata:20240712T143000
DTEND;TZID=Asia/Kolkata:20240712T153000
LOCATION:A-201 (STCS Seminar Room)
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