Sign-Rank vs Margin

Explore a comprehensive lecture on the relationship between sign-rank and margin in boolean matrices. Delve into two fundamental questions: the possibility of lower-bounding margin by a function of sign-rank, and upper-bounding sign-rank as a function of margin. Examine reinterpretations of these questions in the contexts of communication complexity, machine learning, and dimensionality reduction. Discover how Fourier analysis and the Borsuk Ulam theorem are employed to provide strong negative answers to both inquiries. Learn about the applications of these complexity measures in various fields and gain insights from joint research works with Hamed Hatami, Shachar Lovett, and Xiang Meng.