Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.
Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.
Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.
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 pseudo randomness in graphs using eigenvalues and polynomials, emphasizing the significance of bunched roots and common interlacers.
