Keith Ball- Restricted Invertibility

Explore the Kadison-Singer problem and delve into Bourgain and Tzafriri's elegant argument in this lecture. Learn about the Anderson formulation, Hall's marriage theorem, Horn's theorem, and various selection theorems. Discover sharp boundaries, partition selection, and the Source lemma. Examine orthogonal vectors, Groton League's Inequality, and the Garrison Singer Theorem. Gain insights into restricted invertibility and its implications in mathematics.

Intro
The Anderson formulation
Halls marriage theorem
Horns theorem
A lovely result
Sharp boundaries
Choosing a partition
Selection theorems
Source lemma
By orthogonal vectors
Groton Leagues Inequality
Garrison Singer Theorem