Two talks - Bäcklund transformations; The spectra of some arithmetical matrices

There will be two talks in this week's seminar.

Rod Halburd (UCL) - Bäcklund transformations of the anti-self-dual Yang-Mills equations and discrete integrable systems

Alexander Pushnitski (King’s College London) - The spectra of some arithmetical matrices

Abstract for the second talk: I will discuss the spectral theory of a family of infinite arithmetical matrices, whose (n,m)'th entry involves the least common multiple of n and m, denoted LCM(n,m). The simplest example of such matrix is 1/LCM(n,m), where n,m range over natural numbers. It turns out that an explicit formula for the asymptotics of eigenvalues of this matrix can be given. This is recent joint work with Titus Hilberdink (Reading).