These seminars (unless otherwise stated) will take place on **Thursdays at 5pm in Room 106 in Gordon House (29 Gordon Square) **on an (almost) weekly basis** - **see the **link to the map for Gordon House** 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.

## 1st October 2015

##### Rafael Prieto Curiel

**Title: A brief journey through Fractional Calculus**

Abstract:

Differentiating a function is usually regarded as a discrete operator: we use the first derivative of a function to determine the slope of a line that is tangent to it, and we differentiate it twice if we want to know its curvature. We can even "differentiate negative times" a function -integrate it- and thanks to that we measure the area under the curve. But, why stop there? Is calculus bounded to discrete operations, or is there a way to define the half-derivative of a function? Is there even an interpretation or application to half-differentiating a function? Fractional Calculus is a concept, as modern as the traditional version of Calculus, referred to by Leibniz as "a paradox from which one day useful consequences will be drawn". In this seminar a brief introduction to Fractional Calculus will be presented, with some examples and applications

## 8th October 2015

##### Hui Gong

**Title: Algorithmic Trading of Co-Integrated Assets**

Abstract:

This model will be applied as a part of Algo trading strategy for Equities team in Credit Suisse. I will brief introduce the workflow about HOLT Machine Directed Web-tool, which includes three parts.

1. Find out the co-integrated assets in the 'universal'.

2. Determine the optimal weights for each asset, i.e. the optimal investment strategy for an agent who maximizes expected utility of wealth by dynamically trading in these assets.

3. Build the recommendation System based on the forecasting.

I will focus on the second part and show the closed form solution.

## 15th October 2015

##### Artiom Fiodorov

**Title: Probability theory as extension of logic**

Abstract:

In many problems we don't have enough information at hand to permit deductive reasoning. In this talk, I will introduce the idea of plausibility reasoning which focuses on processing incomplete information optimally. I will discuss how any system of plausibility reasoning that satisfies certain commonsense requirements is isomorphic to probability theory. I will examine the requirements carefully and then relate such interpretation of probability to other well-established approaches. Finally, I will look at a wide variety of applications, which include: Thermodynamics (I will show why heat travels from hot to cold objects), Statistics and also... everyday situations!

## 22nd October 2015

##### Pietro Servini

**Title: The Modern Daedalus**

Abstract:

Daedalus was the master craftsman of Greek mythology, building Ariadne's dancing ground, the labyrinth in which King Minos imprisoned the Minotaur (son of his wife's affair with a bull) and, most famously, the wings with which he and his son, Icarus, escaped the cell King Minos had imprisoned them in. In this talk, we focus on flight and, in the context of the stupendous advances that have been made in the century since the Wright brothers' first powered heavier-than-air flight, we ask ourselves where the next advances can be made and what the modern Daedalus might be working on.

## 29th October 2015

##### Belgin Seymenoglu

**Title: Invariant manifolds of a model from Population Genetics**

Abstract:

In 1976, Nagylaki and Crow proposed a continuous-time model for the population frequencies, which focuses on one gene with two variants (or alleles). Much of my time has been spent plotting phase plane diagrams for this model, but whatever values I put in for the parameters, I always find a stubborn special curve in my diagram. This curve is called an invariant manifold, and I have now proven that the manifold does indeed exist in the model, at least for a special case. You can also look forward to a gallery of my colourful phase plane plots which will show that the invariant manifold need not be unique, smooth or convex.

## 5th November 2015

##### Sebastian Bahamonde Beltran

**Title: Teleparallel quintessence with a nonminimal coupling to a boundary term**

Abstract:

In this talk, I am going to briefly introduce the teleparallel equivalent to General Relavitiy and I will talk about a new model in this framework where we consider a scalar field nonminimally coupled to both the torsion $T$ and a boundary term given by the divergence of the torsion vector. This is inspired by the relation $R=-T+B$ between the Ricci scalar of general relativity and the torsion of teleparallel gravity. Then, I will analyse the cosmology of such models using dynamical systems techniques on the case when we have only a pure coupling to the boundary term.

## 12th November 2015

##### James Cann

**Title: Dirichlet's divisor problem**

Abstract:

Moonlighting agony uncle Professor Dirichlet answers your personal problems, …but who does Prof. D turn to in times of trouble? In a letter of 1858 to his contemporary Kronecker, Dirichlet claimed that he had `homed in significantly' on the value of a particular sum which had been causing him issues. However, in true Fermat-style, he gave no further indication to support his claim. This troublesome sum is associated to the divisor function d(m) - the number of natural numbers which divide m. Understanding the asymptotic behaviour of interesting arithmetic functions such as the divisor function is one of the main goals of multiplicative number theory. In this talk we'll get our hands dirty with some good old-fashioned counting, then get a feel for how some of the `greats of mathematics' have used elegant and subtle techniques from analysis to make headway where Dirichlet could not.

## 19th November 2015

##### Erin Sutton

**Title: Syzygies and Manifolds**

Abstract:

Abstract algebra has had many applications throughout its long and varied history, its contributions to topology being a major example. In this talk I will introduce the algebraic notions of resolutions and syzygies before showing how they can be used to analyse certain topological spaces, namely the chain complexes of highly connected universal covers of manifolds with finite fundamental group.

## 26th November 2015

##### Hoi (Justin) Kong

**Title: Ambiguity Aversion to Order Flow**

Abstract:

Electronic Trading Algorithms heavily depend on stochastic models. A model is a framework used for decision making and is exposed to model uncertainty. In this talk, we provide a general overview of model uncertainty (also referred to ambiguity aversion, or Knightian uncertainty) and show how model uncertainty is incorporated in trading algorithms. As a particular example, we show how an agent, who acknowledges that her model of Order Flow is misspecfied, changes her execution strategy to account for model ambiguity when liquidating a large number of shares.

## 3rd December 2015

##### Thomas Boiveau

**Title: Be weak with Nitsche in finite element without penalty**

Abstract:

In computational mechanics, the imposition of boundary conditions is a major challenge, it is therefore crucial to use the right numerical tools to model in the best possible way a given boundary value problem. In this talk, we will introduce the Nitsche's method that is a very useful tool to impose boundary conditions in the framework of finite element. Nitsche's method is a way to impose weakly Dirichlet boundary conditions, this weak imposition allows us to extend the method to more complex problems such that, cut finite element, domain decomposition or fluid structure interaction.

## 10th December 2015

##### Various

**Title: The Postgrad talks Christmas seminar!**

Abstract:

Various PhD students will be giving 5 minute talks on an area of fun or Christmassy maths!