Explore the fascinating world of extreme eigenvalue distributions in sparse random graphs through this comprehensive lecture by Jiaoyang Huang, a member of the School of Mathematics at the Institute for Advanced Study. Delve into topics such as empirical eigenvalue distribution, edge expansion constant, and Roman routing graphs. Examine the universality of distributions, numerical simulations, and the bias towards the negative axis. Gain insights into Gaussian and circular ensembles, spectral result resolution, and the concept of simple switching. Discover how these mathematical concepts apply to real-world scenarios and contribute to the field of mathematical physics.