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

Apply by 28 February 2020 here: https://www.surveymonkey.co.uk/r/RS52ApplnForm

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).

**Main Lecturers: **

Estelle Basor (American Institute of Mathematics) *Operator theoretic methods and their applications*

Tamara Grava (University of Bristol and SISSA) *Nonlinear Hamiltonian PDEs and Painlevé transcendents*

Alexander Its (Indiana University–Purdue University Indianapolis) *Painlevé equations and random matrix theory*

**Clay Lecturer:**Jon Keating (University of Oxford)

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

**Tutorial assistants:**Benjamin Fahs (Imperial College London)

György Gehér (University of Reading)

Kasia Kozlowska (Arup and University of Reading)

**REGISTRATION FEES (INCL. MEALS AND ACCOMMODATION):**

**PhD students**GBP 150 **Early career researchers**GBP 250

**Submitted by Elizabeth Fisher |

**24 / Feb / 2020