Models in Population Dynamics, Ecology, and Evolution (MPDEE) 2020
Date: Monday 20th April 2020 - Friday 24th April 2020
Location: College Court Conference Centre and Hotel, University of Leicester
Abstract: The meeting will consider applications of mathematical modelling to explore processes and mechanisms in various biological systems ranging from a cell to the human society. A special focus will be on the interplay between ecology and evolution across time and space. MPDEE’20 is also expected to explore similarities between modelling techniques traditionally applied in ecology and evolution and those used in other life sciences with the purpose to enhance interdisciplinary approaches and to stimulate further advances in population dynamics, ecology and evolution. The meeting will be an open forum for interaction between theoreticians and empirical biologists with the main goal of enhancing communication between the two groups to better link theories with empirical realities.
The conference is organised by Andrew Morozov and Sergei Petrovskii.
Learn more about ‘Models in Population Dynamics, Ecology, and Evolution (MPDEE) 2020’
Characteristic Polynomials of Random Unitary Matrices, Symmetric Polynomials, and Painlevé Equations
Date: Tuesday 24th March 2020
Location: Ken Edwards LT3, University of Leicester
Abstract: The moments of characteristic polynomials play a central role in Random Matrix Theory. They appear in many applications, ranging from quantum mechanics to number theory. The mixed moments of the characteristic polynomials of random unitary matrices, i.e. the joint moments of the polynomials and their derivatives, can be expressed recursively in terms of symmetric polynomials. These expressions are not easy to compute, however, and so this does not give an effective method for calculating the mixed moments in general. I shall describe a new, alternative evaluation, in terms of solutions of Painlevé differential equations, that facilitates their computation and which allows one to prove previous conjectures concerning their asymptotics when the matrices are large.