Expanders in Higher Dimensions
Irit Dinur (Weizmann Institute of Science)

Expander graphs have been studied in many areas of mathematics and in computer science with versatile applications, including coding theory, networking, computational complexity and geometry.

High-dimensional expanders are a generalization that has been studied in recent years and their promise is beginning to bear fruit. In the talk, I will survey some powerful local to global properties of high-dimensional expanders, and describe several interesting applications, ranging from convergence of random walks to construction of locally testable codes that prove the $c^3$ conjecture (namely, codes with constant rate, constant distance, and constant locality).