Series: Analysis Seminar
Wednesday, February 20, 2019 - 12:55 , Location: Skiles 006 , Steven Heilman , USC , Organizer: Galyna Livshyts
Series: ACO Colloquium
After a brief introduction to classical hypergraph Ramsey numbers, I will focus on the following problem. What is the minimum t such that there exist arbitrarily large k-uniform hypergraphs whose independence number is at most polylogarithmic in the number of vertices and every s vertices span at most t edges? Erdos and Hajnal conjectured (1972) that this minimum can be calculated precisely using a recursive formula and Erdos offered $500 for a proof. For k=3, this has been settled for many values of s, but it was not known for larger k. Here we settle the conjecture for all k at least 4. Our method also answers a question of Bhatt and Rodl about the maximum upper density of quasirandom hypergraphs. This is joint work with Alexander Razborov.
Wednesday, February 13, 2019 - 15:00 , Location: Skiles 006 , Greg Blekherman , Georgia Tech , Organizer: Galyna Livshyts