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SUMMARY:Polytopes and spheres: the enumeration and reconstruction problems
DTSTART:20240122T093000
DTEND:20240122T103000
DTSTAMP:20260510T131932Z
UID:77a2336a34753bfc501e65fbc45a3584ba9fdde1b57a55c20d0d4535
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dr Hailun ZHENG – University of Houston-Downtown\nSeminar in
  Mathematics\n\nConsider a simplicial d-polytope P or a simplicial (d-1)-s
 phere P with n vertices. What are the possible numbers of faces in each di
 mension? What partial information about P is enough to reconstruct P up to
  certain equivalences?\nIn this talk\, I will introduce the theory of stre
 ss spaces developed by Lee. I will report on recent progress on conjecture
 s of Kalai asserting that under certain conditions one can determine P fro
 m the space of affine stresses of P ---- a higher-dimensional analog of th
 e set of affine dependencies of vertices of P. This in turn leads to new r
 esults in the face enumeration of polytopes and spheres\; for example\, a 
 strengthening of (the numerical part of) the g-theorem.\nJoint work with S
 atoshi Murai and Isabella Novik.\n 
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021 https://epfl.zoom
 .us/j/69153870303
STATUS:CONFIRMED
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