MSc thesis presentation - Yennis Ye

Name: Yennis Ye

Date: March 24

Time: 12pm - 1pm

Location: ICCS 204

Supervisor: Joel Friedman

Thesis title: Closures under Span and Intersection of Three and Four Subspaces

Abstract:
Linear information theory leverages linear algebra to study information-theoretic properties of random variables that adhere to a particular linearity constraint. It has an application in coded caching, where the object is to determine how to store information across network nodes so that a central server broadcasts the smallest possible amount of data. In this work, we prove linear algebraic results that can facilitate the derivation of inequalities to improve the lower bound on this minimal broadcast requirement.

Specifically, we examine the closure under span and intersection of families of subspaces within a finite-dimensional vector space. We demonstrate that the closure of three subspaces has a maximum size of 28, while the closure of four subspaces can be unbounded. To prove the latter, we show that the closure of four lines in general position in F^3 is infinite if and only if the field F has characteristic zero.