Videos

Explicit Lossless Vertex Expanders

Presenter
October 27, 2025
Abstract
In this talk, I will describe our construction of the first explicit lossless vertex expanders. These are graphs where every small subset of vertices has about as many neighbors as their sparsity allows. Previously, the strongest known explicit vertex expanders were those given by Ramanujan graphs, whose spectral properties imply that small sets of vertices have only half as many neighbors. An insight of our work is the key role high dimensional expanders play as local-to-global amplifiers of the property of lossless vertex expansion.Based on joint work with Jun-Ting Hsieh, Ting-Chun Lin, Alex Lubotzky, Sidhanth Mohanty, Ryan O'Donnell, and Assaf Reiner.