## Seminars and Colloquia by Series

Wednesday, October 3, 2018 - 12:55 , Location: Skiles 006 , Xingyu Zhu , Georgia Institute of Technology , , Organizer: Galyna Livshyts
TBA
Monday, October 1, 2018 - 15:30 , Location: TBA , TBA , TBA , Organizer: Caitlin Leverson
Monday, October 1, 2018 - 14:00 , Location: Skiles 006 , Lenny Ng , Duke University , Organizer: Caitlin Leverson
Friday, September 28, 2018 - 15:00 , Location: Skiles 005 , , 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.
Thursday, September 27, 2018 - 11:00 , Location: Skiles 006 , , UCLA , Organizer: Mayya Zhilova
Wednesday, September 26, 2018 - 12:55 , Location: Skiles 006 , , Georgia Institute of technology , , Organizer: Galyna Livshyts
I shall tell about some background and known results in regards to the celebrated and fascinating Log-Brunn-Minkowski inequality, setting the stage for Xingyu to discuss connections with elliptiic operators a week later.
Series: PDE Seminar
Tuesday, September 25, 2018 - 15:05 , Location: Skiles 006 , , University of Chicago , , Organizer: Yao Yao
Monday, September 24, 2018 - 14:00 , Location: Skiles 006 , Miriam Kuzbary , Rice University , Organizer: Jennifer Hom
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.
Thursday, September 20, 2018 - 15:05 , Location: Skiles 006 , Konstantin Tikhomirov , School of Mathematics, GaTech , Organizer: Christian Houdre
Let (A_n) be a sequence of random matrices, such that for every n, A_n is n by n with i.i.d. entries, and each entry is of the form b*x, where b is a Bernoulli random variable with probability of success p_n, and x is an independent random variable of unit variance. We show that, as long as n*p_n converges to infinity, the appropriately rescaled spectral distribution of A_n converges to the uniform measure on the unit disc of complex plane. Based on joint work with Mark Rudelson.