The Projective/Injective Ratio and GPTs
Explore the intriguing relationship between projective and injective tensor products of normed spaces in this 39-minute lecture by Stanislaw Szarek at the Hausdorff Center for Mathematics. Delve into the historical context of this problem, from Grothendieck and Pisier's early work to its modern applications in physics and generalized probabilistic theories. Discover how the discrepancy between projective and injective norms is lower-bounded by the power of the smaller dimension, with varying exponents depending on the setup. Examine a range of techniques from geometry of Banach spaces and random matrices used to tackle this problem. Learn about special cases, general cases, and potential areas for improvement in this collaborative research. Gain insights into related concepts such as factorization constants, weak factorization constants, and the mmstar estimate.