**Lent Term 2019**

**This year marks the 100th anniversary of the TMS – the TMS Centenary. For more details on the TMS Symposium and Dinner, please see our TMS Centenary website: http://tms100.uk**

Link to termcard: TMS Lent 2019 Termcard

All talks will take place in the Winstanley Lecture Theatre unless stated otherwise.

**Monday 28 January, **8:30PM

**Solitons: An Introduction**

**Dr Anthony Ashton (DAMTP)**

Solitons are a very special type of solution to some nonlinear, dispersive PDEs. I will discuss some of the history of solitons, as well as some of their remarkable properties. The talk should take us from canal boats to pseudospherical surfaces, with some mathematics in between.

**Monday 4 February, **8:30PM

**Are we living in the matrix?**

**Professor David Tong (DAMTP)**

Here is an interesting fact: no one knows how to write down a discretised version of the laws of physics in a manner that allows them to be simulated on a computer. The obstacle is known as the Nielsen-Ninomiya theorem. I will describe this result and some attempts to circumvent it.

**Monday 11 February, **8:30PM

**The Continuum Hypothesis**

**Professor Imre Leader (DPMMS)**

We’ll explore a statement known as the Continuum Hypothesis, which states that there are no `sizes’ of sets between the natural numbers and the reals — or, more precisely, that every uncountable subset of the reals bijects with the reals.

**Monday 18 February, **8:30PM

**Sum-of-squares proofs**

**Dr Hamza Fawzi (DAMTP)**

A polynomial that is a sum of squares of other polynomials can only take nonnegative values. This trivial observation is surprisingly powerful: many inequalities in mathematics have simple sum-of-squares proofs. I will discuss algorithms that can automatically search for sum-of-squares proofs for polynomial inequalities, and the extent to which they can be considered as “automatic proof machines”.

**Saturday 23 – Sunday 24 February**

**TMS Symposium and Centenary Dinner**

**Various Speakers**

The TMS Symposium is a day of lectures, held in the Winstanley Lecture Theatre, about a wide array of mathematical subjects. This year the Symposium will be split over 2 days. The first day will be dedicated to the history of the TMS, with 10 distinguished speakers, representing or talking about each decade of the TMS. The second day will be for current members of the society to talk about their research and contribution to mathematics.

The TMS dinner is an annual tradition, taking place in the Trinity Old Kitchens, where all members of the society are encouraged to join us in celebrating the TMS. This year, in order to mark the special occasion, the Centenary dinner will be a much grander affair. The dinner will be held in the Great Hall with around 200 guests, both past and current members of the society.

The dinner will take place on 23rd February after the first day of the Symposium. We should be releasing tickets near the start of Lent term, so watch our for that and make sure to get your ticket early! Updates released on tms100.uk.

**Monday 25 February, **8:30PM

**Addition, multiplication, and why they don’t get along**

**Dr Julia Wolf (DPMMS)**

The sum-product conjecture, put forward by Erdős and Szemerédi in the 1980s, states that the set of all pairwise sums and the set of all pairwise products of a finite subset of the reals cannot simultaneously be close to minimal in size. Despite the simplicity of its statement and a significant amount of research effort devoted to its resolution, the conjecture remains open to this day. In this talk I will explain the motivation for the conjecture as well as some fascinating partial results.

**Monday 4 March,** 8:30PM

**Elliptical billiards and Poncelet trajectories**

**Professor Pelham Wilson (DPMMS)**

Given an elliptical billiard table, to any ball trajectory which doesn’t cross the line segment joining the two foci, there is an associated smaller confocal ellipse inscribed in the trajectory. A Poncelet trajectory is one which is closed after a finite number of bounces. We’ll see that if there is one such closed trajectory with n segments, then starting from every point on the outer ellipse, there is a similar closed trajectory with n segments and the same inscribed ellipse, and indeed all these trajectories have the same length

Analogous geometric properties hold more generally for any pair of conics in the plane, and in modern terminology the existence of analogous Poncelet polygons is related to the torsion points on an associated elliptic curve.

**Monday 11 March, **8:30PM

**How to Build Mathematical Models**

**Professor Eric Lauga (DAMTP)**

Everybody knows what “Mathematics” is but ask around and you will quickly realise that nobody really knows what “Applied Mathematics” means. In this talk I will use research drawn from the world of physics and biology to convey what it means to be an applied mathematician. In particular, I will explain how one goes about building a mathematical model, what approximate solutions are and why sometimes you don’t have a choice and need to use a computer.