An Introduction to Lifted Expander Graphs - Fernando Granha Jeronimo

Explore the world of lifted expander graphs in this comprehensive computer science and discrete mathematics seminar. Delve into the construction and analysis of sparse yet well-connected graphs with Fernando Granha Jeronimo from the Institute for Advanced Study. Learn about the lifting operation used to create larger expanders from smaller ones, and discover the near-Ramanujan construction of lifted expander graphs with additional symmetry structure. Understand the implications of this research for coding theory and its potential applications. Examine key concepts such as spectral expansion, universal expansion, and quantum dots, while gaining insights into the intuition behind these complex mathematical structures. This in-depth talk covers topics ranging from degree spectrum and unit layers to representation theory and potential applications in various fields.

Intro
Fake idea
Two lift
Label
Lemon
Deleted Graph
Degree
Spectrum
Unit Layers
Representation
Why this block form
Notation
Trace Power
Spectral Expansion
Universal Expansion
Constructions
Harder Applications
Potential Applications
Intuition
Quantum Dots
Base Graph