Abstract 

In the first part of the talk, I will provide a quick introduction to various types of classical random matrices, including the circular ensembles, Gaussian ensembles, Wishart matrices, etc., along with some classical results regarding the distribution of their eigenvalues. In the second part, I will present our findings concerning extreme gap problems, namely the smalles and largest spectral gaps, for circular and Gaussian random matrices, and propose several conjectures.

MDSC: Mathematical Data Science Centre

The MDSC was created to be a global leader in the development of the mathematical theory of data science, and to train the next generation of mathematical data scientists.

Data science is a rapidly developing area with tremendous impact on everyday life. Nowadays, almost every form of information extraction is labelled data science, and data scientists can be found in every scientific discipline. At the same time, an overwhelming majority of data scientists focus on domain-specific problems rather than on the fundamental understanding of phenomena at the heart of information extraction: namely, when, and why information extraction is possible, and how to make it efficient. Satisfactory answers to those questions require the development of cutting-edge, novel mathematics, which is the main goal of the MDSC.