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Are Matrices the Same as Vectors? Spencer's Theorem and Matrix Spencer Conjecture

Speaker: Chi-Ning
Title: Are Matrices the Same as Vectors? Spencer's Theorem and Matrix Spencer Conjecture
Date: 08 Sep 2022 17:30-19:00 EST
Location: SEC Level 3 NW Terrace
Food: Indian

Spencer’s theorem is a classic result in discrepancy theory where a cute existential proof (using entropy argument!) beats the probabilistic method. However, the same idea doesn’t extend to the “matrix” version of Spencer’s theorem (which is in a “vector” setting) and whether one can still beat the probabilistic method in the matrix case is then know as the “Matrix Spencer Conjecture”.

In this talk, I will first talk about Spencer’s theorem: its setup, its motivations, and the cute proof using entropy. In the second half of the talk, I’ll talk about several recent progresses on proving Matrix Spencer Conjecture and my personal thought on it. Basic familiarity with discrete probability should be a sufficient background to follow the talk.