Hamilton Prize and Lecture 2012
Hamilton Lecture 2012
On Tuesday October 16th 2012, the Royal Irish Academy again presented awards to students of Mathematics in nine of the Higher Education Institutions in Ireland. Each mathematics department were invited to nominate its "best" student in the penultimate year of undergraduate mathematical studies. The recipients of the Hamilton Award in Mathematics received a scroll and a cheque for €1,000 generously sponsored by Google. Eoghan Nolan, Head of European Operations in Google speaking at the prize giving ceremony said “We're delighted to be supporting the Hamilton Prizes, particularly as the work of Hamilton reaches into my own industry where his major mathematical discovery - quaternions - are used today in computer graphics. Advanced science, engineering and mathematics underpins everything we do at Google - whether that's developing a new algorithm, analysing the results of experiments or using data to understand our clients businesses and help them make better business decisions. We are delighted to recognize these remarkable mathematicians and their achievements”.
This event formed part of Hamilton Day activities at the RIA which celebrate Hamilton’s life and contribution to mathematics and usually take place on or around October 16th, the anniversary of the day Hamilton scratched his fundamental formula for quaternion multiplication on Broome Bridge in Dublin.
Hamilton Prize Winners 2012
Back row L-R: Andrew Doran-Sherlock; DIT, Suzanne Burns; UCD, Padraig O’Shea; UL, Alexei Kudryashov; NUIM, James Patrick Fennell; UCC
Front row L-R: Denis Patterson; DCU, Eoghan Staunton; NUIG, Professor Yuri Manin, Professor Luke Drury, Eoghan Nolan, Colman Humphrey TCD
Hamilton lecture 2012
Professor Luke Drury, President of the Royal Irish Academy, President Michael D Higgins, Professor Yuri Manin and Professor Brian Norton President of DIT at the RIA 2012 Hamilton lecture.
This years Hamilton Lecture was given by Professor Yuri Manin, The Max Planck Institute of Mathematics, Bonn, on Tuesday October 16th in Gleeson Hall Theatre, Dublin Institute of Technology, Kevin Street.
Title: Silver lining: codes and clouds
Error-correcting codes, their asymptotic bounds, and Kolmogorov complexity.
Abstract: An error-correcting code C over a given finite alphabet A is simply a set of words of some fixed length n of which one can think as ‘meaningful’ ones, such as
Morse code for letters.
When such a code is used in practice, some input data are translated into a sequence of code words that are then transmitted through a channel with random noise.
There arises a problem: at the output end the initial words must be reconstructed from corrupted words. ‘Good codes’ are those that maximize simultaneously the probability of correct reconstruction and the relative quantity of meaningful words.
In 1981 the author defined and proved the existence of the so called ‘asymptotic bound’: a continuous curve that in a sense determines the boundary for possible good codes. But not a single value of this function is known, and in 2011 the author even conjectured that it might be uncomputable.
In this talk, I will sketch all the relevant techniques and a proof of the recent result (2012, joint with M. Marcolli) showing that a natural partition function involving Kolmogorov complexity allows us to interpret the asymptotic bound as a curve dividing two different thermodynamic phases of codes.