## Michaelmas

**How to hunt a submarine**, by *Dr Tom Körner*

*Wednesday, 29th October 2014, 6pm*

1939-1945.

The Atlantic, Mediterranean and the Pacific – the main theatres of WWII naval warfare.

There was never any doubt that, in that famous war nearly 70 years ago, outcomes for battles in the ocean were as dominating factors as campaigns on the land. Submarines played a critical part in the former, so much so that Nazi Germany built 1,156 U-boats at huge costs to hunt down Allied fleets in the Atlantic and Mediterranean, while US submarines were accountable for 28% of Japanese vessels destroyed in the whole of the Pacific warfare. In response, anti-submarine tactics and technology saw rapid development, which directly contributed the overall Allied victory.

**Stein’s Paradox**, by *Dr Richard Samworth*

*Wednesday, 12th November 2014, 6pm*

Stein’s paradox is one of the most surprising results in Statistics. Suppose X1,…,Xp are independent random variables, with Xi∼N(θi,1). If we want to estimate θ=(θ1,…,θp), the most obvious choice is to use X=(X1,…,Xp). It turns out that, provided p≥3, we can find a better estimator, in a very natural sense that I will make precise. As well as giving the (fairly straightforward) proof, I will discuss geometric intuition, other explanations for this result, and extensions. I will also show how the improved estimator can be used to give good predictions of baseball batting averages.

**Arithmetic**, by *Prof Michael Potter*

*Wednesday, 19th November 2014, 6pm*

What are the natural numbers? Answering this question is harder than you might think. I shall talk about an elegant answer given by Richard Dedekind in 1888, a sense in which his answer was complete, and a sense in which it wasn’t.

## Lent

**P-adic numbers**, by *Kevin Buzzard*

*Tuesday, 27th January 2015, 6pm*

Sometimes if you’re looking for inspiration when trying to solve a horrible differential equation, you might write the solution as a power series and then try to solve for the coefficients to spot what’s going on, without worrying about convergence. If you try doing this with a horrible Diophantine (integer) equation instead, and write down the answers in base p and don’t worry about convergence, you just invented the p-adic numbers. Come to this talk and discover a world where 1+2+4+8+… really does equal -1.

**A Century of Turbulent Motions in Fluids**, by *Colm-cille Caulfield*

*Tuesday, 10th February 2015, 6pm*

In 1915, G. I. Taylor was awarded the Adams Prize at the University of Cambridge for an essay entitled “Turbulent motion in fluids”, and also published a paper entitled “Eddy motion in the atmosphere”, describing observations made in direct response to the loss of the Titanic. In this talk, I will show how the key ideas of these 100-year-old papers remain absolutely central even today to the huge environmental challenge of understanding and modelling turbulent mixing in density-stratified fluids such as the atmosphere and the ocean.

**From lichen to lightning: understanding random growth**, by *Amanda Turner*

*Tuesday, 24th February 2015, 6pm*

Random growth processes arise in a variety of physical and industrial settings, from cancer to polymer creation. Despite their practical relevance, mathematicians and physicists have so far been unable to provide answers to some fairly fundamental questions such as “what does a typical cluster look like?”. We shall explore how the combination of probability and complex analysis can be used to provide a mathematical description of planar random growth.

**The risk neutral world and how to price risk**, by *Dr Matthias Dörrzapf*

*Tuesday, 3rd March 2015, 6pm*

The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk – the notion that the future is more than a whim of the gods and that men and women are not passive before nature.

Peter Bernstein, in *Against the Gods: The Remarkable Story of Risk*

Although this statement is I think not without a certain degree of flamboyancy and prejudice, it does highlight the importance of our rational understanding of risk in the modern society, thanks to the development of probability theory – in particular – over the past centuries. In this talk, I will attempt to define risk quantitatively, and explain how it is viewed/evaluated differently by different individuals. I will then go on to tackle the problem of how financial assets should be priced in a risk-neutral world.

## Easter

**Annual Garden Party**, by *The Adams Society*

*Saturday, 13th June 2015, 12 noon*

Once again, the Adams Society hosted a garden party with plenty of entertainment, food, and Pimms, enjoyed by all who came. Unfortunately, this year, the sporadic rain hurt our attendance somewhat – but nonetheless, we still had many fellows and students show up to enjoy the company and refreshments.

### About Us

The Adams Society is the mathematics society of St John’s college, Cambridge. We host numerous events each year including mathematical talks and socials.

### Talks

Free admission to all talks. Refreshments are served in the foyer before each talk.

Our talks usually take place in the Fisher Building, St John’s College.

### Contact

Get in touch through our committee members or email theadamssociety@gmail.com