The Adams Society hosts numerous events each year. These include mathematical talks by leading academics in the field, and social events making good use of the historical setting. You can find more about our annual social events at John’s Socials, or check out our Past Events and Photo Gallery.

For in-person events, there is the opportunity to join the speaker and some members of the committee in St John’s Hall after the talks. A form where you can easily sign up to dine in hall if you are not from St John’s should be included in the email for each talk, even if it is not yet linked below. Feel free contact a member of the committee if you would like to book a ticket.

### Upcoming and Recent Events

Events 2023–24 can be found here. Remember to sign up to our mailing list to be notified of new events!

## Lent Term

**Catz vs John’s Football Match
**

Sunday 10th Mar, 1pm

John’s Playing Field

6-4 against Catz !!!

**AGM**

Saturday 9th Mar, 3pm

Arthur Quiller-Couch Room

**Entrepreneurship for Mathematicians**

by Dr Ewan Kirk

*Tuesday 12th Mar, 6pm
*

*Boys Smith Room*

As AI, Machine Learning, Statistics, Optimisation and Computer Science takes over the world, mathematicians are the new “rock stars” in the commercial world. The demand for mathematical and statistical skills ranges from huge global tech companies to startups and early stage companies. Indeed, many startups are being founded my mathematicians. The talk will cover the types of skills one needs as an entrepreneur, how to identify good ideas when you have them — and more importantly how to identify a bad idea. How to get started and how to pitch to investors and customers. Many of these skills are valuable in businesses other than startups and learning how entrepreneurial skills will help you whatever your career choice.

As AI, Machine Learning, Statistics, Optimisation and Computer Science takes over the world, mathematicians are the new “rock stars” in the commercial world. The demand for mathematical and statistical skills ranges from huge global tech companies to startups and early stage companies. Indeed, many startups are being founded my mathematicians. The talk will cover the types of skills one needs as an entrepreneur, how to identify good ideas when you have them — and more importantly how to identify a bad idea. How to get started and how to pitch to investors and customers. Many of these skills are valuable in businesses other than startups and learning how entrepreneurial skills will help you whatever your career choice.

**Skyrmions—a Theory of Nuclei**

by Prof Nick Manton

*Tuesday 27th Feb, 5.30pm
*

*Castlereagh Room*

Protons and neutrons are not point-like objects, neither are they “billiard balls”. In an atomic nucleus, they deform and partly merge. Skyrmions accommodate this. They are solutions of equations for the pion fields that mediate forces between protons and neutrons. The mathematics of Skyrmions and their quantum states uses ideas from topology, symmetry groups, and group representations. The main aim of the theory is to understand better the shapes and complicated energy spectra of excited nuclei.

**Statistical Inference for Infectious Disease Modeling**

by Prof Po-Ling Loh

*Tuesday 20th Feb, 6.10pm
*

*Castlereagh Room*

In many scientific problems of contemporary interest, data are acquired in a very heterogeneous and non-i.i.d. fashion: Edges in a network may give rise to important correlations between node-level observations, which must be taken into account when performing data analysis. In large-scale applications, the structure of the graph may also determine the type of algorithms that may be performed. This talk will briefly overview some research problems involving mathematicalanalysis of network-structured data. A central question is how to formulate rigorous statistical theory for data collected over (or in the form of) a network. I will focus on the problems of source inference and graph hypothesis testing.

In the first part of the talk, I will discuss algorithms for inferring the source of a disease spreading over a tree-structured network. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). Given the infection status of individuals at a particular time instance, the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. I will present a method for constructing confidence sets for the source of the infection, with the property that the cardinality of the confidence sets depends only on the error probability and the degree of the nodes in the tree, rather than the size of the infection set. The analysis depends on a careful probabilistic analysis of relative subtree sizes as the infection propagates over the tree, and utilizes the theory of Polya urns.

Next, I will discuss a problem concerning hypothesis testing between graph structures. In this scenario, the goal is to infer the network structure of the underlying graph based on knowledge of which individuals have been infected at a certain time, but not their relative connectivity. However, since the infection information is restricted to a single observation, methods such as graphical model estimation become invalid for inferring the connections between individuals. I will present a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the two graphs involved in the hypothesis test.

This is joint work with my former PhD student Justin Khim, now a researcher at Amazon.

**Knots, Curvature, and Hard Problems**

by Prof Martin Bridson

*Saturday 17th Feb, 5pm
*

*Castlereagh Room*

If you ask “how many…”, the answer should be a number. If you ask “what sort of symmetry…”, the answer should be a group. Because groups describe symmetry wherever it is found, they provide bridges between mathematical contexts. In this talk, they will appear as we pass from the problem of deciding when two knotted pieces of string are the same to the problem of listing all compact models of space and space-time. Along the way, we will consider what it means for a problem to be “hard”.

Charles Dodgson (a.k.a. Lewis Carroll) used the word “knot” to describe any tricky puzzle. He would appreciate this milestone in our discussion: If a knot is not the not-knot, then the group of the knot is not the not-knot group. This was once a theorem of Max Dehn, now it is not; nevertheless, it is true.

*About the Speaker:*Prof Bridson is the Whitehead Professor of Pure Mathematics at the University of Oxford, a fellow of Magdalen College, and President of the Clay Mathematics Institute. His main interests lie in geometric group theory, low-dimensional topology, and spaces of non-positive curvature.

*followed by*

**Annual Dinner**

*Saturday 17th Feb, 7.30pm
Senior Combination Room
(reception kindly hosted by Prof David Stuart in his office at 6.45pm)*

## Michaelmas Term

**Drawing Shapes at Random**

by Prof Wendelin Werner

*Tuesday 21st Nov, 5.30pm
*Castlereagh Room

How do we draw, or choose, shapes at random in a natural way (or more formally stated, what are natural measures on spaces of self-avoiding curves or loops)? In this talk, I will describe a principal open question in this area and explain how complex analysis enters the game when dealing with planar curves.

*About the Speaker:*Prof Werner is the newly appointed Rouse Ball Professor of Maths, and is mainly interested in the application of probability theory and complex analysis to mathematical physics. He received the Fields Medal in 2006 ‘for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory’, among other awards.

**Entropy: From Steam Engines to Black Holes and Quantum Computers**

by Sean Hartnoll

*Tuesday 7th Nov, 5pm
*Boys Smith Room

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.

*About the Speaker:*Prof Hartnoll has been DAMTP Professor of Mathematical Physics since 2021. His research lies in the intersection of high energy, gravitational, and condensed matter physics.

**Categorification**

by Prof Jack Smith

*Tuesday 31st Oct, 5.30pm
*Castlereagh Room

A surprisingly common phenomenon in mathematics is that sometimes a problem gets easier to understand if you make it harder. One fruitful way to do this is to add extra structure to the objects involved: a process known as

*categorification*. In this talk, I will discuss some examples of categorification in action, some familiar and others related to current research problems.

**The Importance of Beautiful Equations: the Life and Work of Paul**

Dirac

by Prof Peter Goddard *CBE FRS*

Dirac

*Tuesday 17th Oct, 5pm
*Boys Smith Room

In his PhD thesis, Paul Dirac established the fundamentals of quantum mechanics. Son after he predicted the existence of antimatter and won a Nobel Prize when he was just 31. Although famously taciturn, he was a close friend on Werner Heisenberg and Robert Oppenheimer. He described St Jon’s as the central point of his life. The talk will give an account of the life and work of the man whom Niels Bohr described as having the greatest scientific mind since Newton.

*About the Speaker:*Prof Goddard is a mathematical physicist who was Master of St John’s from 1994 to 2004. He was formerly Director of the Institute of Advanced Study at Princeton and is currently an Emeritus Professor in the School of Natural Sciences at Cambridge. His interests lie mainly in string theory and conformal field theory, to which he contributed the Goddard–Thorn theorem, among many others.