Since the beginning of the covid 19 pandemic, EMS has started to hold online talks and meetings and some of them are recorded.

You can find these talks below or on the playlist here,

## Susanna Terracini (Feb 18 - 2022, ICMS and Heriot-Watt University)

### Title: Pattern formation through spatial segregation

## Steven Tobias (Jan 21 - 2022, University of Edinburgh)

### Title: From Order to Chaos and Chaos to Order in Fluid Flows

The eleven year solar activity cycle is a remarkable example of regular behaviour emerging from an extremely turbulent system. The jets on Jupiter sit unmoving on a sea of turbulent eddies. Astrophysical phenomena often display organisation on spatial and temporal scales much larger than the turbulent processes that drive them. An outstanding problem of astrophysics (and indeed other branches of nonlinear physics) is the mathematical description of such systems that can capture systematic behaviour emerging from the underlying chaos, given that Direct Numerical Simulation of these objects is simply impossible. These fascinating phenomena introduced and and it is discussed how methods from non-equilibrium statistical mechanics may be developed to give some insight into their behaviour.

## Martin Bridson (University of Oxford) (Dec 10 - 2021, University of Glasgow)

### Title: Finite shadows of infinite groups, finiteness properties, and geometry

There are many situations in geometry and group theory where it is natural, convenient or necessary to explore infinite groups via their actions on finite objects. But how much understanding can one really gain about an infinite group by examining its finite images? Sometimes little, sometimes a lot. In this colloquium talk, it is sketched the rich history of this problem and describe how input from hyperbolic geometry and low-dimensional topology have transformed the subject in recent years.

## Gavin Gibson (Oct 22 - 2021, AGM)

### Title: Data augmentation and imagination

The technique of data augmentation, whereby observed data are effectively augmented by additional quantities not actually observed in an experiment, has proved to be extremely powerful in modern statistics generally, and in Bayesian parametric inference in particular. This talk will describe its application to Bayesian inference for epidemic models where many challenges arise from the typically incomplete observations of epidemic processes.

## Henry Segerman (Oct 1 - 2021, EMS popular lecture)

### Title: Artistic mathematics: truth and beauty

This is about Henry's work in mathematical visualisation: making accurate, effective, and beautiful pictures, models, and experiences of mathematical concepts. He discusses what it is that makes a visualisation compelling, and show many examples in the medium of 3D printing, as well as some work in virtual reality and spherical video. He also discusses his experiences in teaching a project-based class on 3D printing for mathematics students.

## Ernesto Estrada (May 21 - 2021, hosted by ICMS and University of Stirling)

### Title: Postcards from Network Theory

I will show some postcards of the use of network theory for solving real-world problems. After a very brief introduction I will start by illustrating such postcards. The postcard 1 is about the study of protein-protein interaction (PPI) networks. The postcard 2 is about the use of networks to describe the 3-dimensional structure of biomacromolecules. In particular, I will develop the concept of network communicability and its relation to matrix functions. Postcard 3 is about the study of navigation routes on networks and its implication to traffic in cities. I will show how such diffusive processes on graphs can explain the routes followed by drivers at rush hour in several cities across the world. The final postcard is about the development of mathematical strategies to implement nonlocal interactions in networks.

## Anne Skeldon (Feb 19 - 2021, hosted by ICMS and University of Strathclyde)

### Title: Mathematical modelling of the sleep-wake cycle: light, clocks and societal rhythms

We’re all familiar with sleep, but how can we mathematically model it? And what determines how long and when we sleep? In this talk I’ll introduce the non-smooth coupled oscillator systems that form the basis of current models of sleep-wake regulation and discuss their dynamical behaviour. I will describe how we have used models to inform debates on societal questions such as whether to move school start time for adolescents and whether or not countries should move to permanent daylight saving time.

## Dwight Barkley (Jan 11 - 2021, hosted by ICMS and University of Edinburgh)

### Title: A fluid mechanic's analysis of tea-cup singularity

One of the most fundamental issues in fluid dynamics is whether or not an initially smooth fluid flow can evolve over time to arrive at a singularity -- a state for which the classical equations of fluid mechanics break down and the flow field no longer makes physical sense. While proof remains an open question, numerical evidence strongly suggests that a singularity arises at the boundary of a flow like that found in a stirred cup of tea. The goal of this talk is to explain, from a fluid-mechanics perspective, why.

## Stefaan Vaes (Dec 11 - 2020, AGM hosted by ICMS and University of Glasgow)

### Title: Ergodic theory without invariant measures

Ergodic theory deals with dynamical systems from a measurable point of view. One considers transformations of a probability space, like the rotation of a circle over a typically irrational angle. In general, one considers transformations that may or may not preserve the given probability measure, but that will always preserve sets of measure zero. Iterating the transformation, one obtains a nonsingular action of the group of integers. A number of classification results for such nonsingular actions, and also for other groups than the integers, are introduced in this talk.

## James Maynard (Oct 23 - 2020, AGM hosted by ICMS and University of Edinburgh)

**Title: **Approximating real numbers by fractions

How well can you approximate real numbers by rationals with denominators coming from a given set? Although this old question has applications in many areas, in general this question seems impossibly hard - we don’t even know whether e+pi is rational or not! If you allow for a tiny number of bad exceptions, then a beautiful dichotomy occurs - either almost everything can be approximated or almost nothing! James talks about this problem and presents an approach that relies on a fun blend of different ideas, including ergodic theory, analytic number theory and graph theory.

## Sophie Carr (Oct 2 - 2020, EMS popular lecture, part of Maths Week Scotland 2020)

**Title: **What is the best super power?

If you could have any power as a super hero, what would it be? Would you choose to be able to use and interpret statistics? Statistics are an everyday part of life - in our social media feeds, news reports and conversations. It's not always easy to know if we can trust the statistics we're seeing, and that is a problem because at their very best statistics are incredibly emotive: they can be a driving force for change. So if we're going to take on the biggest questions and challenges facing us, we really do need the super power of statistics to help us.

## Kenneth Falconer (May 22 - 2020, hosted by University of St Andrews)

**Title: **Symmetry and Enumeration of Fractals

In this talk, it is discussed how a simple ‘iterated function system’ construction leads to large classes of self-similar fractals. It is described how a little group theory can be used to examine the symmetries of these fractals and to enumerate various classes, with pictorial examples.