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!

Next week’s talk will be given by Prof. Tom Fisher on elliptic curves; details are below. We will again be meeting in the CMS rather than the Winstanley.

Title: Elliptic curves in geometry and arithmetic
Speaker: Tom Fisher
Abstract: Elliptic curves may be regarded as the first non-trivial curves, and admit a rich theory starting with the fact that they are both algebraic curves and groups. In this talk I will start by describing some classical problems in geometry and number theory, before explaining what they have to do with elliptic curves. I will also discuss what is known, and what is expected to be true, about ranks of elliptic curves over the rational numbers.
Date: Monday 26 February
Time: 7pm
Location: CMS, MR2

Next week’s talk will be given by Prof. John Lister on fluid mechanics; details are below. We will again be meeting in the CMS rather than the Winstanley.

Title: Stretching, bending, twisting and coiling: the fluid-mechanical sewing machine
Speaker: John Lister
Abstract: Idlers at breakfast watching a stream of honey falling from a knife, may notice it buckle and coil as it reaches the toast. What happens if you move the toast (or the knife) steadily sideways?  This talk will outline the mathematical description of the dynamics of a falling viscous thread, with possible diversions via chocolate fountains and Viennetta ice-cream.
Date: Monday 19 February
Time: 7pm
Location: CMS, MR2

Next week’s talk will be given by Dr Oliver Janzer on Ramsey theory; details are below. We have not yet determined the location of the talk – it will likely be held in the CMS, but we will send confirmation in a subsequent email.

Title: Ramsey numbers and generalized Ramsey numbers
Speaker: Oliver Janzer
Abstract: An old result in Combinatorics states that in every sufficiently large group of people, there are either 100 people who all know each other, or 100 people who all don’t know each other. But how large does the group need to be to have this property? This innocent-looking question has puzzled mathematicians for decades. In this talk I will discuss this problem and some variants of it.
Date: Monday 12 February
Time: 7pm
Location: TBA, likely CMS.

Next week’s talk will be given by Prof. Wendelin Werner on probability theory; details are below. Note that we will be meeting in the CMS rather than the usual Winstanley.

Title: Drawing at random
Speaker: Wendelin Werner
Abstract: How one can try to draw/choose shapes at random in a natural way (or more mathematically, what are natural measures on spaces of self-avoiding curves or loops)?  I will describe a main open question in this area, some results and explain how complex analysis enters the game when dealing with planar curves.
Date: Monday 5 February
Time: 7pm
Location: CMS, MR2

We hope to see you on Monday!

Hello all,

Unfortunately, the TMS will not be hosting a talk this week. However, we have been asked to promote a ‘mathematical play’ directed by Henry Jaspars, a first-year mathematician at Trinity. The play runs this week as a Corpus Lateshow: further details can be found here.

We will hopefully return to regular programming next week.

Hello all,

Welcome back to Cambridge! We hope you’ve had an enjoyable break.

Our first talk of the term will be given by Prof. David Khmelnitskii on one of his ‘fairy tales’; details are below. Note that, on the request of the speaker, the title will not be announced beforehand. Note also that the talk will take place in the CMS rather than our usual meeting location.

Speaker: Prof. David Khmelnitskii
Date: Monday 22 January
Time: 7pm
Location: MR2 – CMS

We hope to see you on Monday!

Hello all,

Our last talk of the term will be given by Dr Monica Kang of Caltech on operator theory; details are below.

Before the talk on Monday, we will be hosting dinner with the speaker at YORI BBQ. If you are interested and would like to come along, please fill out the form circulated on the mailing list. Details will be confirmed in due course.

Title: Operator algebra in AdS/CFT
Speaker: Dr Monica Kang
Abstract: From the AdS/CFT correspondence, we have a holographic isometric map arising between the local operator algebras of the bulk theory and the boundary conformal field theory. I will explain how operator algebras can naturally be used for understanding spacetime theories in this physical context to unveil some structures of quantum gravity. In particular, I will focus on building the formalism on the bulk reconstruction from the boundary operators to the bulk operators and explain how quantum extremal surfaces aid in studying the relative entropy of the bulk and the boundary. I will further describe how we can understand the formulation in low-dimensions to describe the topology changes of the bulk.
Date: Monday 27 November
Time: 7pm
Location: Winstanley Lecture Theatre – Trinity College

Refreshments will be likely provided following the talk. In addition, Jane Street has asked us to share the following:

Applications for the 2024 Jane Street Graduate Research Fellowship (GRF) are now open! The Fellowship supports exceptional doctoral students currently pursuing a PhD in mathematics, computer science, physics, or statistics.

At Jane Street, we take a rigorous, quantitative approach to trading on global markets, combining techniques from machine learning, distributed systems, programmable hardware, statistics, and applied mathematics. Our culture is steeped in the idea that we will never stop solving; we’re looking forward to supporting technically excellent PhD students who share our core values of intellectual curiosity and humility. Those awarded the Fellowship will receive:

– Full tuition and fees covered for the upcoming academic year.
– A $45,000 USD stipend (or the equivalent in your local currency) to help with living expenses while completing their PhD.
– An invitation to visit our office to give a talk on any topic to Jane Street employees and other Fellowship recipients; all expenses paid.

Full details can be found here.

We hope to see you on Monday!