The continuously growing number of COVID-19 cases pressures healthcare services worldwide. Accurate short-term forecasting is thus vital to support country-level policy making. The strategies adopted by countries to combat the pandemic vary, generating different uncertainty levels about the actual number of cases. Accounting for the hierarchical structure of the data and accommodating extra-variability is therefore fundamental. We introduce a new modelling framework to describe the course of the pandemic with great accuracy, and provide short-term daily forecasts for every country in the world. We show that our model generates highly accurate forecasts up to seven days ahead, and use estimated model components to cluster countries based on recent events. We introduce statistical novelty in terms of modelling the autoregressive parameter as a function of time, increasing predictive power and flexibility to adapt to each country. Our model can also be used to forecast the number of cases, study the effects of covariates (such as lockdown policies), and generate forecasts for smaller regions within countries. Consequently, it has strong implications for global planning and decision making. We constantly update forecasts and make all results freely available to any country in the world through an online Shiny dashboard.

Zoom: https://durhamuniversity.zoom.us/j/91762005266?pwd=VkpLZzNOQUszTGg0c2F2MFdtL21RZz09

Elliptic polylogarithms are analytic functions which play an important role in the study of special values of L-functions of elliptic curves. In the 2000s, Levin-Racinet (and later Brown-Levin) generalized these to multiple elliptic polylogarithms, which are likewise conjectured to be of deep arithmetic-geometric interest. The original definition of multiple elliptic polylogarithms is analytic and uses the complex uniformization of the underlying elliptic curve in an essential way. The goal of this talk is to give an algebraic-geometric definition of multiple elliptic polylogarithms which gives back the original definition after analytification. This is joint work in progress with Tiago J. Fonseca (Oxford).

We discuss the rigidity of measurable subsets in the Euclidean space such that the Lebesgue measure of their intersection with a ball of radius r, centred at any point in the essential boundary, is constant. Based on a joint work with Dorin Bucur.

I shall present two recent pieces of work investigating how shape effects the transport of active particles in shear. Firstly we will consider the sedimentation of particles in 2D laminar flow fields of increasing complexity; and how insights from this can help explain why turbulence can enhance the sedimentation of negatively buoyant diatoms [1]. Secondly, we will consider the 3D transport of elongated active particles under the action of an aligning force (e.g. gyrotactic swimmers) in some simple flow fields; and will see how shape can influence the vertical distribution, for example changing the structure of thin layers [2]. [1] Enhanced sedimentation of elongated plankton in simple flows (2018). IMA Journal of Applied Mathematics W Clifton, RN Bearon, & MA Bees [2] Elongation enhances migration through hydrodynamic shear (in Prep), RN Bearon & WM Durham,

A natural notion of energy for a map is given by measuring how much the map stretches at each point and integrating that quantity over the domain. Harmonic maps are critical points for the energy and existence and compactness results for harmonic maps have played a major role in the advancement of geometric analysis. Gromov-Schoen and Korevaar-Schoen developed a theory of harmonic maps into metric spaces with non-positive curvature in order to address rigidity problems in geometric group theory. In this talk we discuss harmonic maps into CAT(k) spaces which are metric spaces with positive upper curvature bounds. By proving global existence and analyzing the local behavior of such maps, we determine a uniformization theorem for CAT(k) spheres. We highlight how this uniformization theorem relates to the Cannon Conjecture, a major open conjecture in geometric group theory.

This lecture focuses on the scientific legacy of the Arab polymath Alhazen (Ibn al-Haytham; b. ca. 965 CE in Basra, d. ca. 1041 CE in Cairo). A special emphasis will be placed on his mathematical approaches to natural philosophy in the context of his studies in optics, and by way of his geometrization of the inquiries in classical physics and establishing the methodological rudiments of experimentation and controlled testing. To illustrate some of the principal aspects of his geometrical redefinition of the key concepts of natural philosophy qua physics, I shall consider the analytical case of his positing of place (al-makān) as a postulated geometric void in the context of his critical refutation of the definition of topos in Book IV of Aristotle’s Physics.