Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.
Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.
Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.
Explores Belief Propagation in graphical models, factor graphs, spin glass examples, Boltzmann distributions, and graph coloring properties.
Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.
