2018-03-16 | Tsz Chiu Kwok: Operator Scaling and Spectral Analysis
Operator scaling has wide applications in theoretical computer science including permanent approximation, signed rank lower bounds, linear matroid intersection, etc, and is recently receiving a lot of attentions due to its connection with non-commutative ranks and Brascamp Lieb inequality. Recently, we use techniques in operator scaling to solve a basic open problem in frame theory named the Paulsen problem: given vectors u_1, …, u_n in R^d that are nearly Parseval and nearly equal norm, can we change the vectors slightly to v_1, …, v_n so that they become exactly Parseval and equal norm? The fundamental question is whether the total change sum_i ||u_i – v_i||^2 need to depend on the number of vectors n. We answer this question affirmatively.
In this talk, I will present our result on the Paulsen problem, and discuss our recent progress on the spectral analysis of operator scaling.
Tsz Chiu Kwok is currently a postdoctoral fellow at University of Waterloo. His research interests lie in spectral graph theory and more recently operator theory. Before joining University of Waterloo, he was a postdoctoral fellow at EPFL. He obtained his Ph.D. in computer science from the Chinese University of Hong Kong in 2015, and his M.Phil. and B.Sc. in mathematics from the same school.