Seminars and Colloquia by Series

Friday, December 7, 2018 - 15:00 , Location: None , None , None , Organizer: Lutz Warnke
Friday, November 23, 2018 - 15:00 , Location: None , None , None , Organizer: Lutz Warnke
Friday, November 16, 2018 - 15:00 , Location: Skiles 005 , Greg Bodwin , Georgia Tech , Organizer: Lutz Warnke
Friday, November 9, 2018 - 15:00 , Location: Skiles 005 , Sivakanth Gopi , Microsoft Research Redmond , Organizer: Lutz Warnke
Friday, November 2, 2018 - 15:00 , Location: Skiles 005 , Guoli Ding , Louisiana State University , Organizer: Lutz Warnke
Friday, October 26, 2018 - 15:00 , Location: Skiles 005 , Souvik Dhara , Microsoft Research New England , Organizer: Lutz Warnke
Friday, October 19, 2018 - 15:00 , Location: Skiles 005 , Boris Bukh , Carnegie Mellon University , Organizer: Lutz Warnke
Friday, October 12, 2018 - 15:00 , Location: Skiles 005 , Prasad Tetali , Georgia Tech , Organizer: Lutz Warnke
Friday, September 28, 2018 - 15:00 , Location: Skiles 005 , Lutz Warnke , Georgia Tech , Organizer: Lutz Warnke
In 1973 Erdos asked whether there are n-vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integer g \ge 4 for which some g-element vertex-set contains at least g-2 triples.) We answer this question, by showing existence of approximate Steiner triple systems with arbitrary high girth. More concretely, for any fixed \ell \ge 4 we show that a natural constrained random process typically produces a partial Steiner triple system with (1/6-o(1))n^2 triples and girth larger than \ell. The process iteratively adds random triples subject to the constraint that the girth remains larger than \ell. Our result is best possible up to the o(1)-term, which is a negative power of n. Joint work with Tom Bohman.
Friday, September 21, 2018 - 15:00 , Location: Skiles 005 , Yi Zhao , Georgia State University , Organizer: Lutz Warnke
For integers k>2 and \ell0, there exist \epsilon>0 and C>0 such that for sufficiently large n that is divisible by k-\ell, the union of a k-uniform hypergraph with minimum vertex degree \alpha n^{k-1} and a binomial random k-uniform hypergraph G^{k}(n,p) on the same n-vertex set with p\ge n^{-(k-\ell)-\epsilon} for \ell\ge 2 and p\ge C n^{-(k-1)} for \ell=1 contains a Hamiltonian \ell-cycle with high probability. Our result is best possible up to the values of \epsilon and C and completely answers a question of Krivelevich, Kwan and Sudakov. This is a joint work with Jie Han.

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