## Summer 2016

This is the compilation of the talks given in the 2016 Postgraduate (Summer) Seminar Series which was organised by Dan Green.

# Summer 2016

23 Jun 2016, Dan Green

### Any fold will do: The mathematics of origami

In this PSS talk, we'll draw back the curtain, to see for certain, why origami is better than a straight edge and compass, investigating some impossible geometric constructions. From here we'll introduce modular origami, and some of the polyhedra which can be constructed using this method of paper folding. Including some visual examples.
We'll start with a short history of origami, and a set of axioms which explain how we achieve this system which is stronger than a straight edge and compass. Unfortunately, it's not quite the case that ANY fold will do.

In this interactive talk, you, the listener, will get to do some paper folding with coloured paper! There may be red and yellow and green and brown and scarlet and black and ochre and peach and ... and blue paper.

7 Jul 2016, Leonard Hardiman

### Conformal Field Theories

A functorial quantum field theory is a mathematical formulation of string theory that models the interaction of strings through representations of a category of cobordisms. Much of the mathematics I study comes from a particular kind of functorial quantum field theory called a conformal field theory. In the talk I hope to provide a gentle introduction to what a conformal field theory is and explain in broad terms where the mathematics I care about comes in. The talk will be much less technical that this abstract.

### Fun with Gaussian processes

Machine learners tend to use the word gaussian processes (GPs) a lot. If you like overfitting data in a robust manner, then GPs are the way to go. However, they have many other applications. In this talk we shall see how we can use GPs for prediction, dimensionality reduction and differential equation solving.

### Flawed design (or why I can't invent good talk titles).

“Do you think that the television news programmes are impartial about politics?" "What proportion of your evening viewing time do you spend watching news programmes?" "Has anyone attacked or threatened you with anything like a baseball bat, frying pan, hockey stick or rugby tackle?"

What issues can you see with asking these questions in a survey? What biases may you get? What if you had asked the question in a different way?
We'll look at the idea of a general survey design (and its many flaws), what preferential sampling means (hint: it's bias!) and the possible ways around it (and why so many just don't work).

(Vaguely important maths bit: Spatial design of networks and the problem of preferential sampling crops up in a wide range of research areas, from health and air pollution monitoring to meteorology and climate change. Time-permitting, after more fun survey stuff, we'll look at possible frequentist and Bayesian means for overcoming this).

25 Aug 2016, Andrew McRae