The Projective/Injective Ratio and GPTs
Offered By: Hausdorff Center for Mathematics via YouTube
Course Description
Overview
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.
Syllabus
Intro
tensor products of convex sets
Examples
The analogous problem for cones
Special cases
General cases
Circle of ideas
Summary
Factorization constant
Weak factorization constant
Random matrix theory
The mmstar estimate
The power type estimate
Taught by
Hausdorff Center for Mathematics
Related Courses
An Introduction to Functional AnalysisÉcole Centrale Paris via Coursera The Finite Element Method for Problems in Physics
University of Michigan via Coursera Introduction to the Theory of Distributions and Applications
University of Pavia via iversity Методы и инструменты системного проектирования
Moscow Institute of Physics and Technology via Coursera Product Design Using Value Engineering
Indian Institute of Technology Roorkee via Swayam