POSTPONED: Methods for Random Matrix Theory and Applications: LMS-CMI Research School

LMS-CMI Research School

Methods for Random Matrix Theory and Applications

Organised by the London Mathematical Society and the Clay Mathematics Institute, this research school is aimed at postgraduate students and at interested mathematicians, both in the UK and abroad.

Random matrix theory (RMT) is a crossroad of modern mathematics. It brings together and provides a platform for fusing the ideas of such diverse areas as the theory of special functions, orthogonal polynomials, complex analysis, operator theory, representation of affine algebras and quantum group, enumerative topology, combinatorics, number theory, exactly solvable quantum models, quantum chaos and string theory. Simultaneously, RMT plays an increasingly important role in many applied sciences and technologies. Indeed, the distributions of random matrix theory govern statistical properties of the large systems which do not obey the usual laws of classical probability.

Though the random matrices  have been long studied for their applications to multivariable statistics since the work of Wishart and in physics for its application to the level-spacing of highly excited energy levels of nuclei since the work of Wigner, Dyson and others, there has in recent years been a renewed significant interest in this subject. Some of the main reasons for this are: (a) The discovery that a large class of random matrix models are related to completely integrable systems of differential equations of both the Painlevé type  and those of the Kadomtsev-Petviashvili (KP); (b) The relation of the theory of random matrices to the theory of Hankel and Toeplitz determinants; (c) The development of the novel technique – the Riemann-Hilbert method, which yields the solution of a number of the long-standing problems in the field; (d) The discovery of the remarkable fact that the random matrices and the nonlinear Hamiltonian PDEs demonstrate  the same universal features at the relevant critical  and transition regimes. These topics as well as some other important aspects of random matrix theory will be covered in the three lecture courses (five hours each) and in the invited lectures (one hour each).

11 to 15 May 2020 at the University of Reading
Funded by the London Mathematical Society, the Clay Mathematics Institute and the Heilbronn Institute for Mathematical Research
Organized by Igor Krasovsky and Jani A. Virtanen
Contact: j.a.virtanen@reading.ac.uk