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SUMMARY:Sergey Avvakumov (University of Copenhagen)
DTSTART:20210422T120000Z
DTEND:20210422T130000Z
DTSTAMP:20260423T035823Z
UID:DCGParis/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DCGParis/5/"
 >A subexponential size triangulation of ${\\mathbb R}P^n$</a>\nby Sergey A
 vvakumov (University of Copenhagen) as part of Discrete and Computational 
 Geometry Seminar in Paris\n\n\nAbstract\nA practical way to encode a manif
 old is to triangulate it.\nAmong all possible triangulations it makes sens
 e to look for the minimal one\, which for the purpose of this talk means u
 sing the least number of vertices.\n\nConsider a family of manifolds such 
 as $S^n$\, ${\\mathbb R}P^n$\, $SO_n$\, etc. A natural question is how the
  size of the minimal triangulation depends on $n$?\nSurprisingly\, except 
 for the trivial case of $S^n$\, our best lower and upper bounds are very f
 ar apart.\n\nFor ${\\mathbb R}P^n$ the current best lower and upper bounds
  are around $n^2$ and $\\phi^n$\, respectively\, where $\\phi$ is the gold
 en ratio.\nIn this talk I will present the first triangulation of ${\\math
 bb R}P^n$ with a subexponential\, approximately $\\sqrt{n}^\\sqrt{n}$\, nu
 mber of vertices.\nI will also state several open problems related to the 
 topic.\n\nThis is a joint work with Karim Adiprasito and Roman Karasev.\n
LOCATION:https://researchseminars.org/talk/DCGParis/5/
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