Graduate Programs      Graduate Home Ph D Programs Masters Degree Ph D Program Requirements Course Descriptions Current Courses Admissions Current Graduate Students Graduate Student Seminar SIAM Chapter Seminar Recent Graduates Incoming Students Graduate Seminar Jing Zhang Carnegie Mellon University Title: Coloring points on the plane Abstract: We will attempt to solve the following problem: given a countable coloring of the plane, namely a function $f:\mathbb{R} \times \mathbb{R} \to \mathbb{N}$, is it possible to find $A$, $B$ infinite subsets of $\mathbb{R}$ such that $f$ restricted on $A \times B$ is constant? We may or may not succeed. I'll talk about additional possible hypotheses that decide the truth of the statement. For example, continuum hypothesis implies the statement is false and the existence of "sufficiently saturated" ideals on $\mathbb{R}$ implies the statement is true.Date: Tuesday, September 12, 2017Time: 5:30 pmLocation: Wean Hall 8220Submitted by:  Yangxi OuNote: Video will not be recorded.