Using mathematics to understand pandemic strategies Abstract:The years of the COVID-19 pandemic brought a world of difficult decisions for individuals and for governments, and of course many arguments about what was the right thing to do. Many disagreements were based on balancing different forms of harm, either from complex human judgements here, and mathematics can give us a useful framework […]
The Forwards and Backwards of Population Models What can we infer about the history of a population from the patterns of genetic variation that we observe today? There is a long history of mathematical modelling of the demographic dynamics of a population and their effect on the genetic relationships between individuals sampled from that population, but the assumptions imposed to […]
Encoding Fourier multipliers in matrix algebras Fourier multipliers are among the most important operators in analysis. They act on a given function $f$ by pointwise multiplication of its Fourier transform with a fixed function $f (m f pt )^$. This action can be vastly extended using more general notions of Fourier transform via group representation theory. In this talk, we […]
Bi-Lipschitz embeddings and optimal partial transport A bi-Lipschitz embedding of a metric space X into another, Y, preserves relative distances between points, up to a multiplicative error. Usually, one seeks a bi-Lipschitz embedding when X is a metric space of interest, and Y has good geometric properties, since the embedding allows X to inherit these properties. A classical example is […]
The Torelli group: a quick tour In this talk we will give a gentle introduction to the Torelli group of a surface. The talk will survey some of its algebraic properties as well as its connection with low-dimensional topology. Along the way we will highlight some seminal work of Joan Birman and Dennis Johnson, among others. Note: due to technical issues, […]
Maths’ Greatest Unsolved Puzzles While mathematicians are undoubtedly brilliant, and their work is used in all kinds of amazing scientific and technological discoveries, there are still questions they can’t answer. Every mathematical question is a puzzle to be solved, and while there’ll be plenty of puzzles for you to chew on, we’ll also discuss some of the questions that still […]
Orthogonal Sobolev polynomials and spectral methods for boundary value problems on the unit ball Our main objective in this talk is to demonstrate how orthogonal Sobolev polynomials emerge as a useful tool within the framework of spectral methods for boundary-value problems. The solution of a boundary-value problem for a stationary Schrödinger equation on the unit ball can be studied from […]
Exponential asymptotics and applied mathematics Divergent series are the invention of the devil, and it is shameful to base on themany demonstration whatsoever.” – N. H. Abel.The lecture will introduce the concept of an asymptotic series, showing how useful divergentseries can be, despite Abel’s reservations. We will then discuss Stokes’ phenomenon, wherebythe coefficients in the series appear to change discontinuously. […]