These seminars will take place on Thursdays at **5pm **on an (almost) weekly basis in **Room B32 **in the 26 Gordon Square. See the **link to the map for 26 Gordon Square** for further details. Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students. They are generally followed by tea and biscuits in the Mathematics Department Staff Room (Room 606, 25 Gordon Street), up the road from 26 Gordon Square - see how to find us for further details.

## 2 October 2014 in room D103, 25 Gordon Street

##### Peter Kilbride

Title: Freeze Concentration - Mathematical Modelling and Application to Low Temperature Biology

Abstract:

Freeze concentration is the redistribution of solute molecules as a liquid solidifies. As an ice matrix forms through a solution, impurities in the solution are excluded from the ice front. This causes the liquid phase to become more concentrated, with the solid phase becoming a more pure solvent. This effect - known as freeze concentration - is ideal for desalination of seawater or concentrating fruit juices for transportation, however it can be damaging when observed in low temperature biology. This seminar will cover mathematical models for predicting freeze concentration, and apply these models to experimental data.

## 16 October 2014

##### Huda Ramli

Title: Stochastic Modelling in Fluid Dynamics

Abstract:

Most numerical methods for simulating advection-diffusion processes can be split into Eulerian and Lagrangian. The Eulerian method solves the transport equation in a fixed spatial grid, whereas the stochastic Lagrangian approach follows particles through space at every time-step. In this talk I will introduce the numerical methods to determine the trajectories of discrete particles which are governed by stochastic differential equations (SDE). The stochastic ensemble can then be transformed into a continuous probability function using kernel density estimation, in order to synchronize with the Eulerian concentration that is described by the underlying advection-diffusion PDE.

## 23 October 2014

##### Matt Wright

Title: Slowly rotating relativistic stars in the presence of dark energy

Abstract:

In General Relativity there are currently no known solutions to Einstein's equations describing an isolated rotating body. In particular there are no solutions describing the interior of a rotating star which can be continuously matched to an asymptotically flat or empty vacuum exterior. In general the matching conditions are overdetermined. I show how assuming the presence of dark energy in the vacuum exterior, the matching conditions are no longer overdetermined and one can match any slowly rotating star to an asymptotically empty vacuum.

##### Tobias Sodoge

Title: What is a Coisotropic? And if so, how many?

Abstract:

I will give an introductory talk on the the geometric objects I deal with for my thesis. I will make it accessible for everyone.

## 30 October 2014

##### Alessandra Crisafi

Title: Optimal market making in lit and dark pools

Abstract:

We consider a finite-horizon market-making problem in which an agent operates in a dark pool by executing the incoming buy and sell orders. Throughout the entire period, the agent is subject to the inventory risk, which increases as his share holding becomes critically small/large. The market maker can control his inventory by submitting lit-pool limit and market orders. We solve a double-obstacle impulse-control problem and we show that the value function is the unique viscosity solution of the associated system of quasi variational inequalities.

## 6 November 2014

##### Stephen Muirhead

Title: Trap Models

Abstract:

Trap models are random walk models that include some sort of trapping mechanism. This is a broad family of models, covering anything from water percolating through porous media to the problem of the `ant in the labyrinthine'.

Although trap models can be complicated, as is usual in probability there is massive simplification when we pass to the scaling limits. We also observe universality: the same scaling limits describe the long term behaviour of many diverse trap models.

In this talk we consider various examples of trap models and consider their scaling limits. In particular, we pose the key question: Does the scaling limit feel the effect of the traps? And if so, how?

## 13 November 2014

##### John Evans

Title: Awesome Algebra

##### Bin Bin Xue

Title: Vortex Patches

## 20 November 2014 in KLB Room M304

##### Raul Sanchez Galan

Title: Awesome Geometry

##### Yan Long Fan

Title: Microlocal analysis on Dirac operator

## 27 November 2014

##### Hui Gong

Title: Algorithmic Trading and High Frequency Trading

## 4 December 2014

##### Dimitrios Chatzakos

Title: What kind of arithmetic objects live on the hyperbolic plane? (or, how to explain Prime Number Theorem to a geometer)

Abstract:

Analysis on the hyperbolic plane arises in many different arithmetic problems. However, there exists a deeper connection between number theory and curved surfaces. I will try to explain in which sense the geometry of the hyperbolic plane has, itself, an "arithmetic" behavior.

##### Anna Lambert

Title: A spoonful of sugar helps the medicine go down: A mathematical model of glycosylation in cell culture