Talks
The Betty Behrens Seminar on Classics of Historiography
Paul Seaward on "The History of the Rebellion" by Edward Hyde, Earl of Clarendon
The combinatorics of spaghetti hoops
Mon 19 November 2018
Department of Chemistry
A Lecture by Professor Simon Tavaré FRS FMedSci, Department of Applied Mathematics and Theoretical Physics and Cancer Research UK Cambridge Institute.
The final talk in a series of lectures organised by the Cambridge Philosophical Society in the Michaelmas Term 2018.
Abstract: Starting with n cooked spaghetti strands, tie randomly chosen ends together to produce a collection of spaghetti hoops. What is the expected number of hoops? What can be said about the distribution of the number of hoops of length 1, 2, …? What is the behaviour of the longest hoops when n is large? What is the probability that all the hoops have different lengths? Questions like this appear in many guises in many areas of mathematics, the connection being their relation to the Ewens Sampling Formula (ESF). I will describe a number of related examples, including prime factorisation, random mappings and random permutations, illustrating the central role played by the ESF. I will also discuss methods for simulating decomposable combinatorial structures by exploiting another wonder of the ESF world, namely the Feller Coupling. Analysis of a children’s playground game shows that apparently small departures from the Feller model can open up a number of unsolved problems.
Cost: Free
Enquiries and booking
No need to book.
Open to all who are interested, no booking required. Entrance is free to all our Cambridge Philosophical Society Lectures. For further information please contact the Executive Secretary or visit the Society's website
Enquiries: Beverley Larner Website Email: philosoc@hermes.cam.ac.uk Telephone: 01223 334743