The joint PG colloquium will be held on *2pm Friday 01 May 2015* at
ICMS, Edinburgh. It is a great opportunity for maths
postgraduates from different research areas to share mathematical interests and network. Our previous joint
PG colloquium in 2014 between the University of Edinburgh and Heriot-Watt University
PGs proved a great success, and now the second one is surely unmissable!

This year we are excited to have fellow students from the University of Glasgow and the University of St Andrews joining us. Since much of the mathematical research in those four universities is focused on different fields, it is definitely going to be a great experience of academic diversity and integration. There will be 4 short talks on different mathematical topics accessible to an audience of all research backgrounds.

Please arrive *15 mins in advance* so that we could keep to the schedule.

Given a set of polynomials such that the Wronskian has only real roots, are the original polynomials necessarily real? The answer, amazingly, is yes (up to a change of basis).This theorem was proven by Mukhin, Tarasov and Varchenko in 2009 by drawing deep links between algebraic geometry, integrable systems and Lie theory. I will give an outline of the main ingredients that go into their proof and some more recent research that has been inspired by this result.

Thompson groups F, T, and V can be constructed in many ways, making them interesting groups from a variety of perspectives. They were introduced in 1965 by Richard Thompson as counterexamples to the Von Neumann Conjecture and have many applications throughout mathematics. I will demonstrate how F, T, and V can built using fractal geometry and infinite trees, as well as describing their useful characteristics.

Using mathematical methods to understand and model crime is a relatively recent idea that has drawn considerable attention from researchers during the last five years. We propose a differential equations model that describes how the number of criminals evolves in a specific area, while allowing for two distinct criminal types representing major and minor crime. Additionally, we examine a stochastic variant of the model that represents more realistically the “generation” of new criminals. Numerical solutions from both models are presented and compared with actual crime data for the Greater Manchester area. Agreement between simulations and actual data is satisfactory. A preliminary statistical analysis of the data also supports the model’s potential to describe crime. An extension to a full spatiotemporal model involving PDEs is also presented.

Riemann surfaces arise in many different branches of mathematics and physics. Originally, Riemann noticed that it is possible to replace the domain of certain complex functions (such as the complex logarithm), by a surface which is in some sense more natural. In this talk I will explain how basic examples of Riemann surfaces, such as the sphere and the torus, come from certain functions defined on the plane. I will also explain one of the key theorems in the theory of compact surfaces, the Riemann-Roch theorem.

Sounds fun? So why not join us! It's gonna be a great day.