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!

Hello all,

Our talk next week will be given by Dr Zoe Wyatt on PDEs; details are below.

Title: Traveling Waves
Speaker: Dr Zoe Wyatt
Abstract: A central idea in the study of both linear and nonlinear evolutionary PDEs is wave propagation. In this talk I will explain some interesting things we can learn from travelling wave solutions to some progressively more complex PDEs. Since we’re near the end of term, the analysis will be friendly, our functions will be well behaved, and I will also read you the best poem ever written about dynamics.
Date: Monday 20 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:

Jane Street’s 2024 Quantitative Trading and Software Engineering Summer Internships in Hong Kong are currently open and accepting applications! We are hoping to get word out to your club members that might be interested in living and working in Hong Kong. Applications are open now and evaluated on a rolling basis. For more information, please consult the attached flyer.

We hope to see you on Monday!

Hello all,

Our talk next week will be given by Prof. Sean Hartnoll on entropy; details are below.

Title: Entropy: From Steam Engines to Black Holes and Quantum Computers
Speaker: Prof. Sean Hartnoll
Abstract: The notion of entropy was invented in the aftermath of the Industrial Revolution to describe the fact that heat engines could never be perfectly efficient. The irreversible generation of entropy was later understood to occur because everyday macroscopic objects are made up of very many small molecules whose microscopic motion is so complicated that we cannot hope to harness their energy in a useful way. This idea of “inaccessible energy” underpinned Hawking and Bekenstein’s calculation of the entropy of a black hole in the 1970’s: stuff inside a black hole is unknowable to an external observer. As things fall into a black hole it grows, and this is the growth of our ignorance and of entropy. I will describe how, over the past half century, black holes have come to be understood as highly quantum mechanical steam engines. As part of this process, the mathematics of black holes has fed into exciting developments in the seemingly unrelated field of quantum entanglement and quantum computation.
Date: Monday 13 November
Time: 7pm
Location: Winstanley Lecture Theatre – Trinity College

Refreshments will be likely provided following the talk. In addition, there have been slight changes to the Society. We are now sponsored by Jane Street, who have asked us to share the following:

This January, Jane Street is excited to host two in- house programmes, WISE and FOCUS. Details about each programme can be found below. The application deadline is Sunday, 19th November 2023. 

WISE (7th – 10th January 2024 in London) is for first-year undergraduate students who identify as women, transgender, and gender-expansive to spend two days in our London office learning more about who we are, what we do, and how we do it. You will learn about how we use maths, computer science and probability concepts in trading, as well as insight into the different roles that exist within the firm. Jane Street will provide all travel and housing accommodation. Deadline to apply is Sunday, 19th November 2023. 

FOCUS: (10th- 13th January 2024 in London) is crafted for undergraduate students, who self-identify with an underrepresented ethnic or racial minority group. No prior finance experience is required, only an interest in seeing what a career at Jane Street might look like! Over the course of two days, you will participate in classes, discussions, and activities that are structured to provide a broad overview of the work our trading, software development, and strategy and product teams do. Jane Street will provide all travel and housing accommodation. Deadline to apply is Sunday, 19th November 2023. 

Furthermore, following personal circumstances, the previous President has resigned and will be switching roles with the previous Vice President – the updated committee is reflected in the email footer and the TMS’ website.

We hope to see you on Monday!

Hello all,

Our talk next week will be by Professor Andrea J. Liu of the University of Pennsylvania on mathematical biology. Note that we will be in the CMS, with a start time of 6:45pm rather than the usual 7pm.

Title: Persistent homology for understanding protein allostery
Speaker: Andrea J. Liu
Abstract: We know from statistical physics that we need ensembles in order to extract microscopic understanding of collective phenomena. We have designed networks to have properties inspired by protein allostery and by “flow allostery” exhibited by the brain vasculature. By analyzing an ensemble of networks designed to have the similar response, we find that the response is of a topological nature and can be characterized using persistent homology. Our analysis is generalizable to real proteins and produces similar results, suggesting that the characterization of protein allostery can be reduced to the measure of the topological significance of two properties.
Date: Monday 6 November
Time: 6:45pm
Location: CMS MR2

As usual, port and orange juice will be served after the talk. We hope to see you there!