### 5th October 2017 - Benjamin Robinson

#### How to Move a Pile of Sand: An Introduction to Optimal Transport

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.

### 12th October 2017 - Dan Green

#### Polyhedra, here I go again. My my, how can I construct you?

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.

### 19th October 2017 - Hayley Wragg

#### How to shut up that sound - Low frequency wave propagation through a composite medium

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.

### 26th October 2017 - Xavier Pellet

#### Homegenization and Gamma Convergence

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.