This coming Monday, we are delighter to have Professor Imre Leader deliver a combinatorics talk at the CMS. And, do hang around for pizza and port/juice after the talk!

Title: Tournaments
Speaker: Professor Imre Leader
Abstract: Most tournaments are of two types. There are all-play-all tournaments, like many chess tournaments or the group stages of football tournaments, and there are knockout tournaments where one loss eliminates you, like most tennis tournaments or the final stages of football tournaments. We will discuss some interesting things that happen in each of these two.
Date: Monday, 28 October
Time: 7pm
Location: MR2, Centre of Mathematical Sciences

As usual, some members of the committee will be walking over to CMS from Great Court at 6.40pm; feel free to join them!

In addition, the TMS is also partnering with Quant Intuition (https://www.quantintuition.com/), who are kindly offering free access to their educational resources for all TMS members! Contact the membership secretary (Blaise Mo, bm628@cam) for the access code (for identity verification purposes, use your @cam email address, or your email address registered on the TMS mailing list).

Following the AGM held on Saturday, a new TMS Committee has been elected for 2024/2025:

President: Eleanor MacGillivray
Vice-President: Arunav Maheshwari
Secretary: Dylan Toh
Treasurer: Samuel Liew
Membership Officer: Blaise Mo
Constable: Fredy Yip

Over the coming days, you should receive details concerning ticketing for the TMS Annual Dinner, and information about the Garden Party and the Annual Cricket Match will arrive in due course.

On a personal note, I’ve grateful to have been part of the Committee over the past year, and I’ve enjoyed sharing with you all the activities of the TMS. The fact that the AGM had significant attendance and several competitive elections should certainly bode well for the future of the society. I’m glad to be handing over my role to Dylan, who I’m sure will do an excellent job for the next year, and I’m looking forward to seeing how the TMS evolves under the new committee.

– Jason.

The society’s AGM will be taking place on the 27^th of April at 4:30pm in the Blue Boar Common Room. We plan to offer refreshments and pizza to those attending. Elections will be held for the following committee positions:

1. President: The President shall coordinate the Committee and invite speakers.
2. Vice-President: The Vice-President shall book the rooms and aid the President, stepping in as necessary.
3. Secretary: The Secretary shall send weekly emails and publicise events to our members.
4. Treasurer: The Treasurer shall organise sponsorships, apply for College funding and make sure we don’t go bankrupt!
5. Membership Officer: The Membership Officer shall manage membership and organised socials.
6. Constable: The Constable (usually an ex-officer) shall aid the Committee in its functions.

As responsibilities are broadly shared across the committee, most positions will not have a significant time-commitment, and each committee member can effectively contribute to shaping the functions of the TMS. For further information about particular roles, please feel free to contact any of the current committee members.

Only Trinity members may stand for election; if you wish to run for a position, you should prepare a brief speech and notify the President (fy276) of your intention to run in advance of the AGM. I would highly recommend those interested to consider running – so that the traditions of the society can both be preserved and improved upon in future.

I hope you’re all well and enjoying the Easter break. In collaboration with The Archimedeans, the society is pleased to announce the establishment of a new annual lecture in honour of Sir Michael Atiyah, a distinguished mathematician and former Master of Trinity. The inaugural lecture will be given in the first week of term by Prof. Sir Simon Donaldson of Imperial College London; see below for full details.

The Inaugural Atiyah Lecture

Title: Complex numbers, quaternions, octonions and singular spaces
Speaker: Simon Donaldson
Abstract: In the first part of the talk I will discuss the 1958 algebro-geometric paper of Atiyah “On analytic surfaces with double points”, relating smoothings and resolutions of two-dimensional double point singularities. In the second part I will review the quaternion number system, differential-geometric hyperkahler structures on four-dimensional manifolds and the ALE spaces which connect with the first part. For the last part of the talk, I will introduce the octonion number system, the exceptional Lie group G{2} and the corresponding differential-geometric structures on seven-dimensional manifolds. I will discuss some parts of the 2001 paper of Atiyah and Witten “M-Theory dynamics on a manifold of G{2} holonomy”, and questions of current research interest concerning singularities of G_{2} structures.
Date: Thursday 25 April
Time: 5pm
Location: Babbage Lecture Theatre – New Museums Site

Our final talk of the term will be given by Prof. Sir Timothy Gowers on additive combinatorics; details are below. Note that the talk will occur in the CMS on Tuesday 7pm rather than the usual arrangements.

In addition, we will be providing pizza following the talk. Please fill in the form circulated on the mailing list if you intend on attending, so that we have an estimate of numbers.

Title: The hidden structure of sumsets
Speaker: Timothy Gowers
Abstract: If A and B are sets of integers, the sumset A+B is defined to be the set of all integers x+y such that x is an element of A and y is an element of B. This deceptively simple definition opens the door to a large number of deep theorems and interesting open problems. I’ll talk about a few of them.
Date: Tuesday 12 March
Time: 7pm
Location: CMS, MR2

We hope to see you on Tuesday!

Next week’s talk will be given by Dr Dominic Yeo of King’s College London; details are below. Note that the talk will occur on Wednesday 7:30pm rather than the usual time.

Before the talk, we will also be hosting a dinner at 6pm with Dr Yeo at The Ivy. If you are interested and would like to come along, please fill out the form circulated on the mailing list. As places are limited, we will aim to confirm places closer to the date.

Title: Scenery reconstruction
Speaker: Dominic Yeo
Abstract: Suppose that the vertices of an n-gon have each been coloured red or blue. You don’t know the exact colouring and would like to find out. A nearby probability theorist agrees to help you, by performing a random walk on the n-gon, and reading out the list of colours they observe. Is this information enough for you to recover the true colouring, or at least the structure of the true colouring? We’ll discuss aspects of this so-called “scenery reconstruction problem”, including the case of infinite graphs.
Date: Wednesday 6 March
Time: 7:30pm
Location: Winstanley Lecture Theatre – Trinity College

We hope to see you on Wednesday!