Alongside the mathematics, the Andrew Wiles Building, home to Oxford Mathematics, has always been a venue for art, whether on canvas, sculpture, photography or even embedded in the maths itself.
However, lockdown has proved especially challenging for the creative arts with venues shut. Many have turned to online exhibitions and we felt that not only should we do the same but by so doing we could stress the connection between art and science and how both are descriptions of our world.
Oxford Mathematician Andrea Mondino has been awarded a Whitehead Prize by the London Mathematical Society (LMS) in recognition of his contributions to geometric analysis in differential and metric settings and in particular for his central part in the development of the theory of metric measure spaces with Ricci curvature lower bounds.
Part of UK virtual operator algebra seminar: https://sites.google.com/view/uk-operator-algebras-seminar/home
Abstract: John Roe was a much admired figure in topology and noncommutative geometry, and the creator of the C*-algebraic approach to coarse geometry. John died in 2018 at the age of 58. My aim in the first part of the lecture will be to explain in very general terms the major themes in John’s work, and illustrate them by presenting one of his best-known results, the partitioned manifold index theorem. After the break I shall describe a later result, about relative eta invariants, that has inspired an area of research that is still very active.
Assumed Knowledge: First part: basic familiarity with C*-algebras, plus a little topology. Second part: basic familiarity with K-theory for C*-algebras.
The random initialisation of Artificial Neural Networks (ANN) allows one to describe, in the functional space, the limit of the evolution of ANN when their width tends towards infinity. Within this limit, an ANN is initially a Gaussian process and follows, during learning, a gradient descent convoluted by a kernel called the Neural Tangent Kernel.
Connecting neural networks to the well-established theory of kernel methods allows us to understand the dynamics of neural networks, their generalization capability. In practice, it helps to select appropriate architectural features of the network to be trained. In addition, it provides new tools to address the finite size setting.
In the first part of the talk, I will review the basic ideas behind Stein’s method for normal approximation and present a general result which we obtained in arXiv:1706.10251 (joint work with Michel Ledoux and Christian Webb). This result states that for a Gibbs measure, an eigenfunction of the corresponding infinitesimal generator is approximately Gaussian in a sense which will be made precise. In the second part, I will report on several applications in random matrix theory. This includes a proof of Johansson’s central limit theorem for linear statistics of beta-ensembles on \R, as well as an application to circular beta-ensembles in the high temperature regime (based on arXiv:1909.01142, joint work with Adrien Hardy).
