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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, 2017 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Yangxi Ou Note: Video will not be recorded. 