**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.

Please find the TMS Lent 2019 Termcard here – many exciting events planned for this term! That includes our TMS Centenary Dinner and Symposium, as well as numerous excellent speakers.

We hope to see lots of you attending. The next talk is next Monday, given by Dr Anthony Ashton.

# Call My Bluff

It’s our final event of the term – the annual TMS tradition of Call My Bluff! A *prime* time for a poem:

As

two

teams

conjure

definitions

of obscure math

terms; Will the other

team realise which are

true amongst the wrong ones?

**TMS Call My Bluff**

**Date and Location: **Monday 26th November, 8.30pm, Winstanley Lecture Theatre

An annual tradition, held by the TMS, in which a team of freshers test their lying capabilities against a team of other students in a reconstruction of the cult British TV show.

We have two impressive teams for an exciting showdown.

# Rolls, Squares and Hexagons: pattern formation through instabilities – Prof. Michael Proctor (DAMTP)

**Rolls, Squares and Hexagons: pattern formation through instabilities**

**Prof. Michael Proctor (DAMTP)**

**Date and location: **Monday 19 November, 8:30pm, Winstanley Lecture Theatre

It is an experimental fact that when an extended system in a simple amorphous state becomes unstable, the new realised state is typically one exhibiting a pattern. It can be shown even for very complicated physical systems that the dynamical processes near the point in parameter space where stability is lost can be represented by a small number of ordinary differential equations. The form of these equations, and the interactions of any possible patterns that can result from the instability, is strongly influenced, and in many cases determined, by the symmetries of the system being studied. One the symmetry group is known, the different patterns can be identified with different representations of the group. I will discuss a number of examples of varying complexity.

# Approximation on the Real Line – Prof. Arieh Iserles (DAMTP)

**Approximation on the Real Line**

Dr. Arieh Iserles (DAMTP)

Dr. Arieh Iserles (DAMTP)

**Date and location: **Monday 12 November, 8:30pm, Winstanley Lecture Theatre

The purpose of the exercise is simple, to design an orthogonal basis in the space of square-integrable functions on the real line such that the linear map taking the basis to its derivatives is skew symmetric. Such bases possess numerous advantages in the computation of ODEs and PDEs. In this talk, based on a joint work with Marcus Webb, I will completely characterise all such orthogonal systems using Fourier analysis and the theory of orthogonal polynomials. The extension of this work to complex-valued skew-Hermitian `differentiation matrices’ is trivial but it leads to a beautiful outcome, an orthogonal system of rational functions designed (in a different context) almost a century ago by Malmquist and Takenaka and which exhibits some truly miraculous properties.

# Stein’s Paradox – Prof. Richard Samworth (Statslab)

Our next talk will be given by Prof. Richard Samworth.

**Stein’s Paradox**

**Prof. Richard Samworth (Statslab)**

**Date and location: **Monday 29 October, 8:30pm, Winstanley Lecture Theatre

Stein’s paradox is one of the most striking results in Statistics. Although it appears to be a toy problem in mathematical statistics, it turns out to have profound implications for the analysis of modern, high-dimensional data. I will describe both the result and some of its consequences.

# Film Night – Travelling Salesman

Important update – **Professor Samworth’s talk has been rescheduled to the week after (29 Oct)**.

This Monday (22 Oct), we will be hosting our Film Night instead. The film will be ‘Travelling Salesman’ – brief description in a haiku.

*Exciting thriller*

*W**hat might it mean if you solve*

*P equals NP?*

**Film Night – Travelling Salesman**

**Date and Location: **Monday 22 Oct, 8:30pm.Winstanley Lecture Theatre.

There will be some snacks (but no alcohol). We hope to see lots of you there.

# A Simple Proof of a Major Result – Prof. Béla Bollobás

Our first talk will be given by Professor Béla Bollobás – details below. Please note that the location is the CMS (Centre of Mathematical Sciences), not the Winstanley Lecture Theatre.

‘A Simple Proof of a Major Result’

Prof. Béla Bollobás (DPMMS)

Date and Location: Friday 12 October, CMS MR2, 7:00 PM

The solutions of highly rated problems that have remained unsolved for decades tend to be long and complicated. Although this is what we have come to expect, this is not always the case: occasionally a novel approach leads to a remarkably short and beautiful solution. In my talk I shall give a particularly striking example of a simple solution of a notoriously difficult problem emerging out of the blue.

# TMS Fresher’s Squash 2018

Our first event of the year is our Fresher’s Squash, which will be held at 7:30PM on Wednesday 3rd October, at the Junior Parlour in Trinity College. This will be a chance to find out a bit more about the society, meet the committee, enjoy a few nibbles and perhaps pay the tiny £2.50 required for lifetime TMS membership.

# TMS Garden Party 2018

As your series of exams draws to an end,

It’s time to celebrate with all your TMS friends.

With strawberry, chocolate, vanilla and brown bread ice cream,

Join us for our Garden Party on the Fellows’ Bowling Green.

**TMS Garden Party**

Date: **Saturday ****9th June,** **1pm to 3pm**

Location: **Trinity College Fellows’ Bowling Green **(or the Wren cloisters if wet)

The entrance to the bowling green is next to the clock tower in Great Court. There will also be Pimm’s and some other light refreshments.

We hope to see lots of you there!

Best wishes,

Michael Ng

TMS Secretary