These seminars will take place on Thursdays at **5pm **on an (almost) weekly basis in **Room 1.20 in Malet Place Engineering Building**. See the **link to the map for Malet Place Engineering** 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.

## 22nd January 2015

### Tao Gao

**Title: Two-dimensional flexural-gravity solitary waves and their dynamics**

**Abstract:**

The numerical study of fully nonlinear wave propagation through a region of a two-dimensional deep fluid covered by a floating flexible plate was concerned. The nonlinear model based on the special Cosserat theory of hyperelastic shells proposed by Toland (2008) is used to formulated the pressure exerted by the thin elastic sheet. The symmetric solitary waves including elevation and depression branches previously found by Guyenne & Parau (2012) and Wang et al. (2013) were quickly reviewed. A new class of hydroelastic solitary waves which are non-symmetric in the wave propagation direction was then computed. We focussed in detail on the stability properties of all solitary waves subject to the longitudinal perturbations. A series of numerical experiments were performed to show the non-elastic behaviour of two interacting stable solitary waves. The large response generated by a localised steady pressure distribution moving at a speed slightly below the minimum of the phase speed, which was called the transcritical regime in literature, was examined. The excitations of multi-packet solitary waves by multiple loads moving with the speed in the transcritical regime suggest new laboratory experiments.

## 29th January 2015 - *postponed to 12th Feb 2015*

## Wednesday 4th February 2015 in KLB M304

### Speaker: Niko Laaksonen

**Title: Applications of Landau's Formula**

**Abstract:**

In 1911 Landau proved his famous asymptotic formula for an exponential sum over the nontrivial zeros of the Riemann zeta function. This formula is a striking example of the relationship between prime numbers and the zeros of the zeta function: it is able to detect prime powers among the set of all real numbers. We will show how this formula can be used to obtain mean value estimates for $L$-functions in the critical strip.

On the other hand, in hyperbolic geometry we know that the lengths of prime geodesics bear a strong resemblance to our usual prime numbers. It turns out that it is possible to obtain analogous behaviour to Landau's formula by considering an exponential sum over the eigenvalues of the Laplacian. We will also see how this exponential sum relates to hyperbolic lattice counting.

## 12th February 2015

### Belgin Seymenoglu

**Title: Elastic and Microelastic Waves**

**Abstract:**

This presentation focuses on elastic and rotational waves coupled together in a nonlinear model of Continuum Mechanics, which includes displacements and microrotations (simply referred to as rotations). The Cosserat coupling term from linear Cosserat models is introduced, and a nonlinear Cosserat coupling is proposed. This new coupling term is then combined with Boehmer and Tamanini's model (2013) to create a new Cosserat model. With this proposed model, I can analyse the effect of the Cosserat coupling on wave propagation in an elastic medium, which is done by determining the equations of motion and finding their wave solutions. An animation of these waves is also provided.

## 19th February 2015

### Speaker: Kwok-Wing Tsoi

**Title: Invitation to Iwasawa Theory**

**Abstract:**

In this talk, I am going to discuss the classical Iwasawa Theory. Firstly, I will introduce the Iwasawa algebra and re-interpret elements of it as p-adic measures. Then I will describe how the p-adic L-function is defined and formulate the Main Conjecture (which is now a theorem by A.Wiles and B.Mazur). Finally, I will discuss some arithmetic consequences of the Main Conjecture. If time permits, I will talk about how these ideas can be employed to develop the Iwasawa theory for CM elliptic curves and its application to the celebrated Birch and Swinnerton-Dyer Conjecture.

## 26th February 2015

### Speaker: Yupeng Jiang

**Title: Real-Time Risk Management: An AAD-PDE Approach**

**Abstract:**

We apply adjoint algorithmic differentiation (AAD) along with PDE methods to manage the risk exposures associated with holding derivative securities. With simple examples, we show how AAD can be applied to both forward and reverse PDEs in a straightforward manner. In particular, in the context of a one-factor default intensity model, we show how one can compute price sensitivities more accurately and much faster than with standard finite-difference methods by combining (i) the adjoint of a forward PDE solver for calibrating the parameters of the intensity model, (ii) the adjoint of a backward PDE solver for pricing the derivative security, and (iii) the implicit function theorem.

## 5th March 2015

### Speaker: Matthew Scroggs

**Title: ****Wool, Paper and Other Distractions from My PhD**

**Abstract:**

During my time as a teacher and my time as a PhD student I have spent too much time being distracted from work by irrelevant maths and mathematical activities. In this talk I will present some of the highlights of my procrastination, including flexagons, modular origami and braiding. I will be bringing my box of wool and paper with me so that after the talk you can all help me waste yet another evening not working.

## 12th March 2015

#### NO SEMINAR

## 19th March 2015

### Speaker: Huda Mohd Ramli

**Title: Quantitative evaluation of numerical integration schemes for Lagrangian particle dispersion models**

**Abstract:**

Motivated by the goal to improve stochastic Lagrangian particle dispersion models (LPDM) in turbulent flows, a numerical solution scheme for their corresponding Fokker-Planck equation (FPE) is presented. The solutions will serve as a benchmark to evaluate integration schemes for the LPDMs. A series of one-dimensional test problems are introduced, for which the FPE is solved numerically using a finite- difference discretization in physical space, and Hermite function expansion in velocity space.

## 26th March 2015

### Speaker: Adam Townsend

**Title: One way of modelling suspensions in viscoelastic fluids**

**Abstract:**

Suspensions of particles in fluids can be found both in nature and as the basis of many products in industry, for example, blood, proteins, ceramics, paper manufacturing, paint and adhesives. The key question, in both theory and practice, is how to predict and understand the macroscopic behaviour of these suspensions (e.g. particle aggregation rate, effective viscosity) by considering their microscopic properties (so looking at hydrodynamic and lubrication forces and Brownian motion). We can see that particles suspended in viscoelastic, non-Newtonian fluids (e.g. whipped cream, printer ink) behave differently to those in Newtonian fluids. Here I'll show you one way to introduce non-Newtonian-ness into Newtonian simulations, by introducing polymer chains! By setting the force laws on these chains, we can simulate a variety of viscoelastic background fluids. In this talk I shall briefly outline the method, show some simulations, and discuss the advantages and disadvantages of this simulation technique. And I will only mention chocolate fountains once.