### 8th February 2018 - James Green

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The next seminar in the Postgraduate Seminar Series will be:

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All seminars take place on **Thursdays at 10:15-11:05** in the **Wolfson Lecture Theatre** (4 West 1.7), unless otherwise stated.

A full schedule of seminars for the 2017-18 academic year is available below.

**There are still spaces available to speak in Semester 2. Please let me know as soon as possible if you would like to give a talk.**

All seminars take place on **Thursdays at 10:15-11:05** in the **Wolfson Lecture Theatre** (4 West 1.7), unless otherwise stated.

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**Thursdays at 10:15-11:05** in the **Wolfson Lecture Theatre** (4 West 1.7), unless otherwise stated.

How do you transport a pile of sand into a hole with minimal effort?

This problem has a rich history, dating back to 1781, during which time a beautiful mathematical theory has been developed, impacting several fields of mathematics and finding applications in subjects that include economics, crowd motion and weather forecasting.

In this talk, I will give a mathematical formulation of the problem, giving meaning to the 'sand', 'hole', and 'effort' mentioned above, and I will present some of the most celebrated results in the area, touching on a few applications along the way.

From school, we’ve learnt about folding or unfolding a cube from or into a net. But can the same be done with other polyhedra, and how many different nets are there for each shape? In order to answer these questions, we consider what a net is, and for that matter, what a polyhedron is.

There are a number of different classes of polyhedra, and we begin this talk with an introduction to these different types, some of the history behind them, and how we can construct different polyhedra from the same initial seed.

Having brushed up on polyhedra, we venture onto constructing nets, making use of children’s toys, paper folding, and a little graph theory along the way.

A question often asked by people around me is how to shut up an annoying noise.

The damage from low frequency noise is a particular concern in settings such as factories. A device featured at the Limerick Industry Study Group has been fairly successful in attenuating this noise, although the physics were not well understood.

In this talk, I will introduce the device and the forms it takes, then present the macro- and microscale models which were formulated at the study group. The modeling considers transmission losses, dissipation and attenuation through a fluid and flexible solid.

This problem incorporates some fluid mechanics with wave propagation, where I will assume the fluids to be Newtonian and touch on the case with non-Newtonian fluids.

Composites are two or more materials with markedly different physical or chemical properties, categorized as matrix or reinforcement. We are interested in performing this discrete to continuum derivation for several particle systems, in the framework of Gamma convergence, a convergence concept for the energies of the systems.

In this talk I will start from a pure mathematical theory, "Geometric measure theory", and model a physical phenomenon, "fracture mechanics". More precisely I will expose a homogenisation theorem for the (αε,βε)-Mumford Shah functional energy associated to a purely brittle composite. Our analysis is focussed on the coefficient for the volume part αε= 1 and the coefficient for the surface part βε. We study for different rates of convergence of βε → 0 the Γ-limit.

Keywords: Γ-convergence, multiscale analysis, free-discontinuity problems, homogenisation, fracture mechanics.

Did you know that the number of people who drowned by falling into a swimming pool correlates with the number of films that Nicolas Cage has appeared in? Chances are you probably don't believe that one of these has caused the other, but you'd be surprised at how many people do!

This talk will first look at the many hilarious ways that people have confused the two concepts (with pictures!). I'll then introduce the notion of causality via an approach based on the framework of potential outcomes known as the Rubin Causal Model (RCM). This involves estimating a treatment effect by considering the difference between the outcome actually observed and that which might have (but didn't!) happen. I'll first frame this problem in the classical context of a simple randomised control trial.

The problem becomes considerably more difficult in the case of observational studies in the presence of confounding factors - those that influence both the dependent variable and independent variable causing a spurious association. I'll discuss ways to overcome this that fit within the rigorous framework of the RCM introduced previously.

Finally, I'll explain why these approaches break down completely when it comes to my research topic (turns out river flows are complicated!) and some vague ideas about how we might manage to sneakily work around it - willing to take suggestions from the floor...

Weather is a topic never far from our thoughts. It is therefore understandable why the inaccuracy and unreliability of weather forecasting can be so frustrating - everyone loves a rainy barbecue, right?

Lewis Fry Richardson was one of the first to propose that weather forecasting could be achieved by solution of differential equations back in 1922. Since then it has evolved immeasurably, with improvements to accuracy and time to solution.

In this talk, I attempt to defend the efforts of forecasting and illustrate why it is so difficult to accurately model atmospheric dynamics - even after much progress. I will introduce the fundamental equations and give an overview of how they are tackled numerically, as well as discussing several of the difficulties which must be circumvented in the process. I shall also attempt to explain the constraints in place which increase the difficulty of the problem and hopefully restore your faith in the humble weather forecaster.

In 1948, C.E. Shannon published "A Mathematical Theory of Communication", founding what has become known as Information Theory. Nearly 70 years later, Shannon's ideas underlie the modern world: long-range communication, data compression and tweets threatening nuclear war (typed with small hands) were all made possible thanks to Information Theory.

My talk will introduce the basics of information and entropy, their applications, and how they lead to a geometric view of statistics - Information Geometry.

What does it mean for two mathematical objects to be equal? I shall present two different answers to this question: a classical answer from set theory and a more modern answer from category theory. I plan then to illustrate why I prefer the latter and illustrate how it is impossible for set theory to capture the categorical notion of equality.

Note: While the one of the definitions is categorical in nature, no prerequisites are assumed. Indeed, I designed this talk in an attempt to illustrate the categorical philosophy without discussing specifics.

6W 1.1

What makes an animal the most successful organism on the earth? Surely, representing 15-20% of the total biomass of terrestrial animals or having colonised almost all the land area make you a good candidate. And there is no doubt that agriculture, farming, slavery, democracy and other complex forms of development were crucial in order to achieve such supremacy. I am afraid, however, that this talk will disappoint you if you are still hoping to be one of those animals. I will explain how the second most successful animal on earth can try to understand what makes an organism a *super-organism* (again, not us sorry) and why mathematics sometimes is our best, or last, resource to achieve this.

In this talk I will point out some of the strengths and limitations of mathematical modelling in the context of collective animal behaviour. This will involve exploring the blurred frontier known as mathematical biology, where meaningful scientific models and fun mathematical toys are largely confused.

Around 1960, random graph theory was founded by the Hungarian mathematicians Paul Erdös and Alfréd Rényi, trying to answer combinatorial questions related to graphs by using random graphs. The field has since then expanded tremendously and it is used not just for theoretical purposes, but for understanding the behaviour of large, complex networks as well.

In my talk, I will consider a simple model for populations, where colonies live and interact in a one-dimensional space, inspired by the well-known Erdös-Rényi graph. We look at some results and conjectures concerning the size of percolation clusters (the size of interacting communities) in this model, closely related to other work regarding spatial epidemics.

10:15 - 12:05

Previously on the PSS XMaths Special, postgrads worked in teams to find obscure answers in a Pointless quiz. This year, it’s a free for all, with individual clickers, dynamic leaderboards, and even more questions to be answered, drawing inspiration from other gameshows.

Questions range from Maths, to Christmas with little in between. Prizes will include (and may be limited to), that warm feeling of destroying the competition.