### Recordings

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.

## Prof. Mark Jerrum (Queen Mary University London) 22 Mar 2024

### Title: Perfect sampling, old and new

The possibility of obtaining perfect samples efficiently from a complex probability distribution entered the consciousness of the community in the mid-nineties with the invention of `coupling from the past’ by Propp and Wilson. The study of perfect samplers of course has considerable theoretical appeal. But, in addition, their ‘self clocking’ aspect may have practical advantages. For example, to obtain (imperfect) samples by direct Markov chain simulation we need an a priori analytic bound on the mixing time of the Markov chain, which even now may be very weak; in contrast, a simulation by coupling from the past halts as soon as a perfect sample has been computed. Coupling may occur much earlier than the analytic mixing time bound might suggest.

In the last decade or so, a remarkable variety of perfect samplers have come to light, too many to survey in one talk. To cut down the scope to something reasonable, I’ll focus on perfect samplers that have the additional property that they are able to sample perfectly (a finite window onto) a random configuration of infinite spatial extent, such as one finds in statistical mechanics. Coupling from the past has this property, as does an approach that Konrad Anand (a PhD student at QMUL) and I have been investigating, and which we are calling `lazy depth-first sampling’. I feel this approach gives a particularly concrete account of what it means for an infinite system to have a unique Gibbs measure.

## Prof. Benjamin Doyon (King’s College London) 16 Feb 2024

### Title: The emergence of hydrodynamics in many-body systems

One of the most important problems of modern science is that of emergence. How do laws of motion emerge at large scales of space and time, from much different laws at small scales? Hydrodynamics offers a basic but very relevant example. Molecules in air simply go along their journey following Newton’s equations. But when there are very many of them, the solution to these equations becomes extremely complicated; seeking the knowledge of each molecule’s individual trajectory is completely impractical. Happily it is also unnecessary. At our human scale, new, different equations emerge for aggregate quantities: those of hydrodynamics. And these are apparently all we need to know in order to understand the weather! Despite its conceptual significance, the passage from microscopic dynamics to hydrodynamics remains a notorious open problem of mathematical physics. This goes much beyond molecules in air: similar principles hold very generally, including in other physical systems such as quantum gases and spin lattices, where the resulting equations themselves can be very different. In particular, integrable models, where an extensive mathematical structure allows us to make progress, admit an entirely new universality class of hydrodynamic equations. In this talk, I will discuss in a pedagogical fashion the general problem and principles, and some recent advances in our understanding, including those obtained in integrable models.

## Prof. John Baez (University of California, Riverside) 8 Dec 2023

### Title: Category Theory in Epidemiology

“Stock and flow diagrams” are widely used for modeling in epidemiology. Modelers often regard these diagrams as an informal step toward a mathematically rigorous formulation of a model in terms of ordinary differential equations. However, these diagrams have a precise syntax, which can be explicated using category theory. Although commercial tools already exist for drawing these diagrams and solving the differential equations they describe, my collaborators and I have created new software that overcomes some limitations of existing tools. Basing this software on categories has many advantages, but I will explain three: functorial semantics, model composition, and model stratification. This is joint work with Xiaoyan Li, Sophie Libkind, Nathaniel Osgood, Evan Patterson and Eric Redekopp.

## Prof. Raúl Tempone (RWTH Aachen University and KAUST) 24 Nov 2023

### Title: Navigating the Unknown: Harnessing Uncertainty in Renewable Energy and Heart Health

Uncertainty Quantification (UQ) emerges as a guiding force in the turbulent sea of data-driven domains, from energy to health. This talk presents a methodology that harnesses UQ for robust renewable energy forecasting, employing a stochastic differential equation model that sails beyond the challenges of wind and solar predictability. Shifting the focus to biomedical imaging, we unveil a novel UQ approach that dives into the depths of MRI analysis, providing more precise insights into cardiac health without being anchored to specific segmentation techniques. Embark on a voyage that highlights how navigating the uncertainties of today with UQ can steer us toward the precision of tomorrow’s applications.

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

### Title: Pattern Formation Through Spatial Segregation

Abstract Goes Here

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

### 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) 10 Dec 2021 – hosted by 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 (Heriot-Watt University) 22 Oct 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 (Oklahoma State University) 1 Oct 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 (CSIC-UIB) 21 May 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 (University of Surrey) 19 Feb 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 (University of Warwick) 11 Jan 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 (KU Leuven) 11 Dec 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 (University of Oxford) 23 Oct 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 (Bays Consulting) 2 Oct 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 (University of St Andrews) 22 May 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.