# Modelling and data analysis of epidemics

The study of infectious disease is one of the largest and most developed areas of mathematical biology. Yet the innate complexity of disease dynamics, the growth of many forms of available data and pressing real-world issues mean that this area is still rich with problems across a range of mathematical areas.

This talk will be focused on influenza. For seasonal influenza (the usual type of ‘flu that circulates each winter), the challenges lie in understanding viral evolution in highly dynamic population models. For pandemics, past and recent data allows detailed exploration of the spatial dynamics, but raises many more questions. The hope is that modelling work will help mitigate the damage of future pandemics.

Professor Julia Gog, University of Cambridge

# Upside-Down and Inside-Out: The Biomechanics of Cell Sheet Folding

Deformations of cell sheets are ubiquitous in early animal development, often arising from a complex and poorly understood interplay of cell shape changes, division, and migration. In this talk I will describe an approach to understanding such problems based on perhaps the simplest example of cell sheet folding: the “inversion” process of the algal genus Volvox, during which spherical embryos literally turn themselves inside out through a process hypothesized to arise from cell shape changes alone. Through a combination of light sheet microscopy and elasticity theory a quantitative understanding of this process is now emerging.

Professor Raymond Goldstein, University of Cambridge

# Collaborative Industrial Mathematics in Europe

Mathematics is not border-bound, and this is true in particular for industrial mathematics, as can be seen from the success of the European Consortium for Mathematics in Industry (ECMI). I will briefly sketch the evolution of the so called European Study Group with Industry (ESGI) and a recent collaborative effort: MI-NET, which is funded by the EU Cooperation for Science and Technology (COST).

MI-NET has for four years provided a financial support framework to industrial mathematics, supporting ESGIs, STSMs and Industrial Workshops. MI-NET has given a boost to Industrial Maths activities all over Europe, especially in Inclusive Target Countries (ITCs). I will give examples of Industrial Maths problems I have encountered, being a small part of this adventure.

Associate Professor Poul Hjorth, Technical University of Denmark

# Singular Formation in 3D Euler Equations and Related Models

Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is a long-standing open question in mathematical fluid dynamics.

Recent computations have provided strong numerical evidence that the 3D Euler equations develop a finite time singularity from smooth initial data. I will report some recent progress in providing a rigorous justification of the singularity formation in the 3D Euler equations and related models.

Professor Thomas Hou, California Institute of Technology (Presenter of the IMA Lighthill Lecture)

# Extracting Order from Disorder: Periodic Orbits Buried in Fluid Turbulence

Ideas from dynamical systems have recently provided fresh insight into transitional and weakly turbulent flows. Viewing such flows as a trajectory through a phase space littered with simple invariant ('exact') solutions and their stable and unstable manifolds has proved a fruitful way of understanding such flows. Central to this approach is identifying such exact solutions directly from turbulent flow data. I will discuss amongst other things recent attempts to harness Koopman operator theory in this quest.

Professor Richard Kerswell, University of Cambridge (Presenter of the Stewartson Memorial Lecture)

# The mathematical theory of geophysical flow models - challenges and some results

The mathematical and numerical analysis of models for atmospheric flows is still a formidable mathematical challenge. The semi-geostrophic equations are a particular system of partial differential equations, widely used in the modelling of large-scale atmospheric flows. In this talk I will review the mathematical ideas and results that have enabled spectacular progress in the past 25 years, as well as discuss the many problems that are still open.

Professor Beatrice Pelloni, Heriot-Watt University

# Applying mathematics to understand our changing climate

Global temperatures are about 1C warmer than they were before emissions of greenhouse gases by human activities started to alter our climate. Month-after-month we see the devastating impacts of extreme weather around the world with, in many cases, the risk of occurrence increasing because of climate change. The higher the warming, the greater the risk. If warming continues at the present rate, we are likely to exceed 1.5C sometime between about 2030 and 2050, and we are on course to exceed 3C of warming by the end of the century.

In this talk, I will discuss how we are using mathematics – from classical dynamics to the latest developments in machine learning – to understand our changing climate and the risks posed to human society.