Friday, June 14

Abstract: I will discuss the problem of classifying completely integrable structures on the complex projective plane, and related problems about Markov triples, such as Frobenius' conjecture that each Markov number occurs at most once as a minimum.

Abstract: For nearly a century, the eigenvalues of random matrices have formed a rich playground for probabilists and mathematical physicists. Yet random matrices of different kinds arise in a much broader range of mathematical fields. I will aim to survey a number of important results and open problems in random matrix theory, with a special emphasis on its interface with areas such as operator theory, graph theory, group theory, and geometry.