These seminars (unless otherwise stated) will take place on **Thursdays at 1pm in Maths Room 706 **(25 Gordon Street) on an (almost) weekly basis ** - **see the map for further details. Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students.

## 11 January 2018

### Speaker: Atheeta Ching

**Supervisor(s): Dr Stephen Baigent**

##### Title: Atheeta Vs. Predator

**Abstract:**

Competitive population systems are special in that there exists a unique, invariant manifold with some great properties! For example, all solution trajectories in the phase plane are actually asymptotic to one on this manifold meaning all non-trivial behaviours occur on this manifold. Our work explores if this still exists in systems where the species co-operate, or perhaps one becomes a predator/parasite...

## 18 January 2018

#### NO SEMINAR

## 25 January 2018

### Speaker: Emily Maw

**Supervisor(s): Dr Jonny Evans**

##### Title: Vanishing cycles

**Abstract:**

I will talk about singularities, and how we can understand them via their so-called vanishing cycles. This topic beautifully illustrates how symplectic topology links algebraic geometry to low-dimensional topology. We will meet some basic examples, and hopefully get to "pinwheels", which are what I am studying! The talk will be highly nontechnical and mostly involve pictures, so should be accessible to all

## 01 February 2018

### Speaker: Yongjo Lee

**Supervisor(s): Dr Christian Boehmer**

##### Title: Soliton deformational wave solutions for nonlinear Cosserat micropolar elasticity

**Abstract:**

After brief introduction of classical continuum and micro-continuum theory, I will show you how the equations of motion can be obtained from various energy functionals. In turn, these equations of motion lead to the soliton solutions via so-called double sine-Gordon equation. And I will show how the solutions can determine the overall deformational behaviour.

## 08 February 2018 in Room 500

### Speaker: Sean Jamshidi

**Supervisor(s): Prof Ted Johnson**

##### Title: Coastal outflows into a buoyant layer

**Abstract:**

River water discharging into the ocean is a major source of sediments, nutrients and pollutants, and as such can both help and hinder the extraordinary variety of life that blooms in coastal regions. It is therefore important for conservationists and oceanographers to understand where river water goes, and the mechanisms by which it is transported. In this talk, I will provide an overview of these mechanisms, focussing particularly on the role played by potential vorticity. I will try to provide as much physical intuition as possible, while also giving a flavour of the mathematics that has been used to study this interesting and rich problem.

## 15 February 2018

### Speaker: Matteo Capoferri

**Supervisor(s): Prof Dmitri Vassiliev**

##### Title: Solving the wave equation: a gentle introduction to microlocal analysis

**Abstract:**

In my talk I will address the following question: can we solve explicitly the wave equation in curved space? Discussing why the answer is not absolutely straightforward will give me the chance to introduce the basic concepts and tools of microlocal analysis.

The talk will be highly non-rigorous, aimed at a general mathematical audience: rather than constructing a precise theory, my goal is to give a flavour of the underlying ideas.

## 22 February 2018

#### NO SEMINAR

## 01 March 2018 at 1pm in room 500

### Speaker: Stephanie Chan

**Supervisor(s): Prof Andrew Granville**

##### Title: Some arithmetic statistics of elliptic curves: a special family

**Abstract:**

Given a random elliptic curve E:y^2=x^3+Ax+B, how many rational points does it have? The minimalist conjecture asserts that 50% have rank 0 and 50% have rank 1. But it turns out that even numerical evidence is hard to obtain. Not only computing rank itself is a hard problem, but the average rank of the first 2,000,000 curves gives a seemingly increasing function. We picked a special family of elliptic curves, those with torsion subgroup Z/2ZxZ/8Z, and carried out some computations. I aim to give a brief introduction to elliptic curves, followed by an overview of some known results in this area (both theoretical and computational), and compare with the data we obtained for this special family. This is joint work with Jeroen Hanselman (Ulm) and Wanlin Li (Wisconsin-Madison).

## 08 March 2018

#### NO SEMINAR

## 15 March 2018

#### NO SEMINAR

## 22 March 2018

### Speaker: Hugo Castillo Sanchez

**Supervisor(s): Prof HJ Wilson**

##### Title: The fluid mechanics of Thixotropic-Visco-Elasto-Plastic materials

**Abstract:**

Many foods, personal care products, paints, ink, adhesives, waxy oils, gels, fluids of biological interest (such as blood), pharmaceuticals, just to name a few, fall into the category of TVEP materials, which are substances that display a combination of three time-dependent complex rheological behaviour: viscoelasticity, thixotropy and plasticity.

In this talk, I will explain in a simple way, with simple maths and imaginary experiments, each of these complex phenomena. In addition, a common non-Newtonian model used to describe the flow of TVEP materials will be shown. Time permitting, I will give a brief introduction to my current PhD research.

The talk will be full of dimensionless numbers along with some awesome histories and curiosities about these rheological phenomena And of course, those that attend the seminar will have the opportunity to win a thixo-plastic candy (or in other words, a chocolate).