The Wonderful World of Plumes, by Dr Colm-cille Caulfield
Wednesday, 4th November 2009, 6pm
Isolated sources of buoyancy or “plumes” are ubiquitous in nature across a vast range of scales, from self-organizing plankton to volcanic eruptions. They exhibit a beautiful variety of dynamical behaviours, which are both important to understand, and fascinating to consider. This talk will discuss some of the mathematical approaches that can be used to model plume dynamics, as well as some of the many reasons why plumes are so significant.
Card Shuffling and Probability, by Dr Nathanael Berestycki
Wednesday, 3rd February 2010, 6pm
Suppose you are given a deck with 52 cards. It is intuitive that if you shuffle it sufficiently many times, the order of the cards will be random uniform. But how many times should you really shuffle it?
In this informal talk we will discuss some math related to this question. Quite apart from being of practical interest (obviously for magic tricks and casinos, but also in genetics), it leads to some beautiful mathematics ranging from probability to representation theory. In particular we will discuss the famous “cutoff phenomenon” discovered simultaneously by Aldous and Diaconis around 1982, which says that (roughly speaking) if the size of the deck is large, then there is a phase transition between a state where the deck is “far from random” and a state where it is “fully random”.
The Class Number One Problem, by Dr Tom Fisher
Wednesday, 10th February 2010, 6pm
A long standing conjecture in number theory, with its origins in the work of Gauss, states that the only imaginary quadratic fields with class number 1 are those with discriminant -3, -4, -7, -8, -11, -19, -43, -67 and -163. The first proofs that this list is complete were obtained independently by Baker and Stark in the 1960’s. Without assuming any prior knowledge of number fields or class numbers, I will describe several different reformulations of the problem, and indicate some of the ideas used to solve it.
Adams Society Garden Party
Wednesday, 9th June 2010, 12 noon
Our annual garden party is one of the highlights each year. Come to enjoy some nice snacks, Pimm’s and other drinks; Relax in the soothing music and summer sunshine, and have a friendly and intelligent chat with the fellows and fellow mathmos of the college. We will also play some croquet to add to the fun.