Expanders in Higher Dimensions: From Local to Global Properties and Applications

Explore the fascinating world of high-dimensional expanders in this 39-minute MUNI Seminar Series talk by Irit Dinur. Delve into the generalization of expander graphs, which have applications across mathematics and computer science. Discover powerful local to global properties of high-dimensional expanders and their diverse applications, from random walk convergence to the construction of locally testable codes proving the c3 conjecture. Learn about key concepts such as Markov chains, error-correcting codes, Ramanujan expanders, and abrotics building. Gain insights into the connections between global dynamics, linear subspaces, and fast mixing of Markov chains in the context of high-dimensional expanders. Conclude with a comprehensive summary that ties together these advanced mathematical concepts and their practical implications.

Introduction
What are Expanders
Markov Chains
Global Dynamics
Error correcting code
Encoding
Linear Subspaces
Expander Code
Expander Graphs
Highdimensional Expanders
Ramnujan Expanders
Abrotics Building
Local to Global Property
Fast mixing of Markov chains
High dimensional expanders
PCP
Local to Global
Summary