16 – 20 May 2022

University of Reading, UK

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).:

Organisers:
Igor Krasovsky, University of Reading
Jani A. Virtanen, University of Reading

Main Lecturers:
Estelle Basor (American Institute of Mathematics)
Tamara Grava (University of Bristol and SISSA)
Alexander Its (Indiana University–Purdue University Indianapolis)

Clay Lecturer: Jon Keating (University of Oxford)

Guest lecturer: Diane Holcomb (KTH Royal Institute of Technology)

Tutorial Instructors:
Benjamin Fahs (Imperial College London)
György Gehér (University of Reading)
Kasia Kozlowska (Arup and University of Reading)

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More information on the research school website