Our final talk – yes, final talk! – of this year is given by Professor Eric Lauga. Details below, hope to see lots of you there!

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 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 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”.

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 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.

This academic year marks the 100th anniversary of the Trinity Mathematical Society. As a result, our usual annual dinner has been upgraded to the TMS Centenary Dinner in Trinity’s Great Hall. This will take place at 7:30PM on Saturday 23rd February, following the Centenary Symposium, and given this special occasion, we shall invite both members of the TMS who are resident junior members of the University and past members (alumni) to raise our glasses to the first 100 years of the UK’s oldest extant subject society.

As opposed to previous years, tickets will be allocated via a ballot rather than on a first-come first-serve basis, and will cost £20. There will be around 100 tickets issued in total for current members, and you are cordially invited to apply at: https://alumni.trin.cam.ac.uk/events/events-2019/tms-2019.

Applications are open and will close on Friday 8th February at 1PM. Once tickets are allocated following the ballot, successful applicants will be required to fill in a form asking about dietary requirements and then pay into the TMS accounts. This information is summarised below:

TMS Centenary Dinner

Date and Time: 23rd February 2019, 7:30PM
Venue: Trinity Great Hall
Cost: £20 for current members
Dress Code: Black tie preferred
Menu: See below

This is a members-only event; if you are not already a member, you can join the TMS for life for only £2.50 at any of our events.

Reminder: Tickets are to be allocated via a ballot, *not* on a first-come first-served basis. Applications will close at 1PM on Friday 8th February. Successful applicants will receive a confirmation email on Friday afternoon.

Remember to check out our Centenary website at http://tms100.uk/ for further updates.

This should be a hugely exciting celebration, so good luck to all applicants!

Menu

TMS Centenary Dinner – 23rd February 2019

Starter
Assiette of Beetroot
(Milk, Sulphites, Celery, Mustard)

Mains
Radwinter Venison loin with Parmesan Crust served with Roasted Butternut Squash, Garlic Creamed Kale and Truffle Scented Mash Potato
(Cereal, Milk, Sulphites, Celery, Mustard, Soya)

(V) Tartiflette with Baked Figs & Balsamic served with Roasted Butternut Squash, Garlic Creamed Kale

Dessert
Chocolate and Passion fruit Bavarois with Crème Anglaise
(Cereal, Egg, Milk, Soya)

For information concerning the TMS Centenary Celebration, please visit the website: http://tms100.uk/

A list of speakers is now available – see the table below for the provisional timetable.

For the talk abstracts, please visit http://talks.cam.ac.uk/show/index/33747

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.