BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Hamilton spheres in 3-uniform hypergraphs - John Haslegrave (Unive
 rsity of Warwick)
DTSTART:20180201T143000Z
DTEND:20180201T153000Z
UID:TALK96853@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Dirac's theorem states that any n-vertex graph with minimum de
 gree at least n/2 contains a Hamilton cycle. Rödl\, Rucinski and Szemeré
 di showed that asymptotically the same bound gives a tight Hamilton cycle 
 in any k-uniform hypergraph\, where in this case "minimum degree" is inter
 preted as the minimum codegree\, i.e. the minimum over all (k-1)-sets of t
 he number of ways to extend that set to an edge. The notion of a tight cyc
 le can be generalised to an l-cycle for any l at most k\, and correspondin
 g results for l-cycles were proved independently by Keevash\, Kühn\, Mycr
 oft and Osthus and by Hàn and Schacht\, and extended to the full range of
  l by Kühn\, Mycroft and Osthus. However\, l-cycles are essentially one-d
 imensional structures. A natural topological generalisation of Hamilton cy
 cles in graphs to higher-dimensional dtructures is to ask for a spanning t
 riangulation of a sphere in a 3-uniform hypergraph. We give an asymptotic 
 Dirac-type result for this problem. Joint work with Agelos Georgakopoulos\
 , Richard Montgomery and Bhargav Narayanan.\n
LOCATION:MR12
END:VEVENT
END:VCALENDAR