# Abstracts

**Sophie Carr,** Bays Consulting

*My travels with maths: Knowing where I am and where my food came from*

In all walks of life, knowing where you are, and frequently more importantly where you are in relation to where you want to be is not always easy. Increasing access to geo referenced data can help - navigation aids are almost standard on smart phones whilst continual developments in analytics and computation means driverless cars become an ever closer reality. But how else can big data and analytics help get you and your supplies to where they need to be without getting lost in the analysis itself? This presentation will discuss recent projects on understanding where you are when there is no GPS signal and how working out where your mussels and chips came from isn’t always as easy as it sounds.

**Eva-Maria Graefe**, Imperial College London

*There’s a hole in my quantum bucket*

The world of our daily experiences is governed by the laws of classical physics. The microscopic constituents that make up the macroscopic world, however, are governed by the very different laws of quantum mechanics. Over the course of the last century a powerful mathematical toolbox emerged that helps us understand the subtle connection between the two theories.

One thing that quantum and classical objects do have in common is that they do not spontaneously vanish, but have to be somewhere at all times. However, we are not always interested in or able to keeping track of the whole universe. Instead, we often focus on a particular region instead. Take for example the interior of a bucket. If the bucket is in a good condition its contents will stay inside. Such small but closed quantum systems are most commonly investigated.

But what if there was a hole in the bucket? If one keeps track of the bucket and its surroundings, the content will still not be lost. If one focuses on the interior of the leaky bucket only, however, the content effectively reduces or vanishes. In quantum mechanics there is an elegant mathematical description of the interior of a leaking bucket called non-Hermitian quantum mechanics which has in recent years become very popular. In this talk I will give a brief overview over the field and its quantum-classical correspondence.

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Alessandra Caraceni**, University of Bath

*The scaling limit of random outerplanar maps*

Since the early 90s, a connection has been drawn between sequences of discrete combinatorial objects (graphs, trees, maps) with growing complexity and corresponding continuous models. In particular the seminal work of Aldous, identifying the CRT (continuum random tree) as the scaling limit of random plane trees, has led to a whole new field of research, and the idea of looking at discrete objects as avatars of some universal, continuous model has found applications in many areas, including combinatorics, stochastic analysis, statistical mechanics and quantum gravity.

The scaling limit of a number of classes of planar maps is the so-called “Brownian Map”; under certain conditions, however, one witnesses different asymptotic behaviours, and certain planar maps with a unique macroscopic face admit the CRT as a scaling limit. This is the case of outerplanar maps, that is maps whose vertices all belong to one external face; thanks to a bijection by Bonichon, Gavoille and Hanusse, we shall show how a uniform random outerplanar map with n vertices, appropriately rescaled by a factor 1/\sqrt{n}, converges in law (in the Gromov-Hausdorff sense) to 7\sqrt{2}/9 times the CRT.

**Sibylle Schroll**, University of Leicester

*Graphs and Representation Theory*

Graphs are not only important combinatorial objects they are also closely linked to, for example, oriented surface (as their 1-skeleton). Another area of mathematics where graphs play an important role is the representation theory of finite dimensional algebras.

In this talk we will give an overview of how graphs and their generalisations, hypergraphs, underpin several areas of representation theory.

**Christl Donnelly**, Imperial College London

*What have numbers ever done for you?*

There have been a lot of bad news stories about infectious disease lately. The largest Ebola epidemic the world had ever seen unfolded in West Africa. Zika virus, previously thought to be little - if any -threat, gave rise to a Public Health Emergency of International Concern. However, there are good news stories. In total, there have been six, yes 6, cases of poliovirus cases caused by wild poliovirus globally so far in 2017. That is the smallest number in a 6-month period that the world has ever seen.

Statistical and mathematical analyses are front and centre in the global flights against infectious diseases. I will highlight examples – explaining the challenges (computational, methodological, and data-related) faced and the most important achievements. I will look back as well as forward and speculate on what the future holds.