Shih Yu Chang
Nice talk, some questions:1. Why use Green functions as tools for your proof in the locations of the nontrivial extremal eigenvalues \lambda_2 and \lambda_N? Besides Stieltjes transformation, can you use other transforms? Laplace transform?2.How do you know that 27% of d-regular graphs are Ramanujan graphs?3. How to apply interlacing polynomials techniques to improve your bounds?4. How about Stieltjes transforms of the semicircle distributions for other ensembles, e.g., Gaussian unitary ensemble, Gaussian symplectic ensemble.