These seminars (unless otherwise stated) will take place on **Thursdays at 5pm in Room 112 in Foster Court **on an (almost) weekly basis** - **see the **link to the map for Foster Court** 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) - see how to find us for further details.

## 14th January 2016

#### NO SEMINAR

## 21st January 2016

#### NO SEMINAR

## 28th January 2016

##### Speaker: Agustin Moreno

**Title: Brief introduction to symplectic fillings of contact manifolds**

Abstract:

I will sketch very broadly and informally what we mean by a contact manifold being fillable by a symplectic one, what different types of fillings that we can look at, and some obstructions to the existence of such fillings. Time permitting, I will mention algebraic torsion in the context of Symplectic Field Theory, and how it relates to my research.

Furthermore, I have attached a spreadsheet showing the current list of speakers and the dates for their talks. I hope you find it useful.

## 4th February 2016

#### NO SEMINAR

## 11th February 2016

##### Speaker: Rafael Prieto-Curiel

**Title: Quantifying the Perception of Security**

Abstract:

Perhaps we all have experienced the fear of being the victim of a crime, but are those fears justified? How do we determine whether a place is secure or insecure? Based on data, a metric to determine whether a region is secure or insecure is developed, and then, having a quantitative approach on the perception of security allows us to compare between different time periods or regions, but it also allows us to determine the relationship between the perception of security and different crime rates or even other regional attributes, such as the amount of street lighting or the population density.

## 18th February 2016

##### Speaker: Momchil Konstantinov

**Title: A Very Quick Dip into Symplectic Topology**

Abstract:

In this talk I will introduce the topic of Symplectic topology - a relatively new subject which has attracted tremendous interest and effort in the last 30 years and produced many striking results. One of the main tools to attack questions in this field is Gromov's theory of Pseudoholomorphic curves which has been then used to define many algebraic invariants - quantum cohomology, Floer cohomology, Symplectic Field Theory and others. We will concentrate on Floer cohomology for Lagrangian intersections and, time permitting, we'll see a specific calculation due to Evans and Lekili in the case of the Chiang Lagrangian in $\mathbb{CP}^3.

## 25th February 2016

##### Speaker: Hugo Castillo Sanchez

**Title: Stability analysis of rheology of worm-like micellar solutions**

Abstract:

In this talk, I will make a brief introduction to a non-Newtonian model (which is called the BMP model, that is used to describe complex fluids that present flow-induced changes in their internal structure such as polymer-like micellar solutions and liquid cristal polymers) and the chemistry behind micellar solutions.

In 1873, a thermodynamic equation that was able to describe gases, liquids and liquid to gas-phase transition under a given set of pressure, temperature and volumen conditions, was derived by Johannes Diderik Van der Waals. A stability analysis of shear stress versus shear rate curves (in simple-shear flow) of worm-like micellar solutions was made using Van der Waals' thermodynamical approach, along with the BMP model. Chaos and bifurcation theory, chemical kinetics, thermodynamic and mechanical potentials will be useful to me to explain and analyse non-linear phenomena which were observed on this research, such as multiple-steady states, phase-coexistance, phase-transition, critical point and shear-banding.

## 3rd March 2016

##### Speaker: Matthew Scroggs

**Title: Solving PDEs is hard, so let's make a computer do it for us**

Abstract:

For many PDE problems, there is no known way to find the exact solution. In these cases we need fast methods that can closely approximate the solution.

In this talk, I will be giving a brief introduction to Finite Element Methods (FEM) and Boundary Element Methods (BEM), two methods that convert PDE problems into easier-to-solve finite-dimensional matrix problems. I will be presenting some interesting features of using BEM on Maxwell's equations for electromagnetism, including the use of matrix preconditioning to improve the quality of the method.

## 10th March 2016

##### Speaker: Luca Scarpa

**Title: Parabolic Stochastic PDEs**

Abstract:

Several well-posedness results for deterministic parabolic PDEs still do not have a corresponding counterpart in stochastic analysis. The aim of the seminar is to present some possible extensions of the classical framework to the case of SPDEs, using tools of monotone and convex analysis.

More precisely, I will point out the main difficulties that must be faced in the stochastic case and I will provide some examples of SPDEs that can be solved in terms of existence-uniqueness-continuous dependence. Moreover, I will also give some insights into the main open problems in this field.

## 17th March 2016

##### Speaker: Pietro Servini

**Title: Theseus in the Labyrinth**

Abstract:

Thus Pasiphae gave birth to Asterion, the minotaur, and Daedalus constructed the labyrinth to imprison him. And every year (or nine, depending on the teller), the Athenians, defeated by King Minos in revenge for the death of his son, would have to send seven young men and seven young women as food for the beast. Until Theseus, son of King Aegeus, Aethra and the god Poseidon, entered the labyrinth.

In 1904, Ludwig Prandtl threw open the door to an age of tremendous advances in our understanding of fluid flow and unwittingly constructed the maze, which has been filled with "innumerable paths with windings" [Ovid] by researchers since. With the string given to us by the beautiful Ariadne, and armed with dynamic roughnesses, we will enter the labyrinth to seek out our minotaur-the phenomenon of flow separation-and discover its fate.

## 24th March 2016

##### Speaker: Alexander Doak

**Title: A brief introduction to free-boundary problems in the complex plane**

Abstract:

We start with assumptions: "Consider a two-dimensional, inviscid, incompressible and irrotational fluid flow". Under such conditions, the velocity vector **u **can be described by a velocity potential, satisfying Laplace. Despite this linear governing equation, the inclusion of a free-surface (some boundary where two liquids meet, such that the boundary is an unknown of the problem) plunges us back into non-linearity. Fortunately, thanks to the theory of analytic functions, these problems can be solved via incredibly accurate and efficient numerical schemes and, in a few instances (under the assumption of no gravity and surface tension), an exact solution can be found.