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URL:/combinatorics-and-optimization/events/tutte-colloq
 uium-jane-gao-1
SUMMARY:Tutte colloquium-Jane Gao
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:Evolution of random graph orders and their di
 mensions\n\nSPEAKER:\n Jane Gao\n\nAFFILIATION:\n University of Ą¶Ż®ŹÓʵ\n
 \nLOCATION:\n MC 5501\n\nABSTRACT: A poset is a set X equipped with a part
 ial order. In this\ntalk I will briefly review the literature of different
  models on\nrandom orders. Then we discuss a particular model called the r
 andom\ngraph order. The random graph order is classical model to generate 
 a\nrandom causal set\, which was introduced in physics to model and\nanaly
 se the space-time universe.Ā \n\nWe will focus on an open problem proposed
  by Erdos\,Ā Kierstad and\nTrotterĀ on the evolution of the dimensions of 
 random graph orders.\nThis problem has been studied by Albert and Frieze\,
  and by Erdos\,\nKierstad and Trotter around 1990. Better bounds on the di
 mensions were\nobtained by Bollobas and Brightwell in 1997\, for ā€œnon-sp
 arseā€\nrandom graph orders. We study the last piece of the puzzle\, in t
 he\nbipartite case\, by investigating ā€œa transition phaseā€ that was\np
 redicted to occur in the sparse regime by Bollobas and Brightwel\, and\nwe
  prove a negative result to their prediction. We expect that a\nsimilar ph
 enomenon would occur in the nonbipartite case.\n\nThis talk is based on a 
 collaborated work with Arnav Kumar.Ā \n\nĀ \n\nĀ \n 
DTSTAMP:20250516T165800Z
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