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SUMMARY:Trees of nuclei and bounds on the number of triangulations of S^3
DTSTART:20151127T141500
DTEND:20151127T153000
DTSTAMP:20260916T153706Z
UID:d7dfc54c3f782016af81f3fc98f34a516bde7204d7fc1335977202b6
CATEGORIES:Conferences - Seminars
DESCRIPTION:Maher Younan\n\n	 \nIn 1962\, W. Tutte showed that the number
  of 2d triangulations (simplicial decompositions) of the sphere S^2 with t
  triangles grows exponentially with t. The equivalent question in 3d remai
 ns open. We introduce a notion of nucleus (a 3d triangulation with boundar
 y such that all nodes are external and each internal face has at most 1 ex
 ternal edge). A nucleus is typically a triangulation with knots along its 
 internal edges.We show that every triangulation can be built from trees of
  nuclei. This leads to a new reformulation of the above question: We show 
 that if the number of rooted nuclei with t tetrahedra grows exponentially 
 with t\, then so does the number of all triangulations of S^3.\n\n	 
LOCATION:MA 10
STATUS:CONFIRMED
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