THE ROYAL IRISH ACADEMY IS IRELAND'S LEADING BODY OF EXPERTS IN THE SCIENCES AND HUMANITIES

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Hamilton Day 2013 and 2012

The 2013 Hamilton Lecture, 'Twistor Theory: A Developing Hamiltonian Legacy', was delivered by Sir Roger Penrose, Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of Oxford University.

About Sir Roger Penrose

Sir Roger Penrose, Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute of Oxford University, is a well known promoter and communicator of science in England. Penrose is perhaps best known for his work on singularities, having developed and supported the hypothesis that black holes are formed from the collapsing cores of dying stars. His theorems, taken in conjunction with those of his colleague Steven Hawking, form the basis of our current understanding of singularities and the black holes which they create.

Penrose's accomplishments do not just range over cosmology, however. His has also made significant contributions to maths, physics and even philosophy. He is deeply interested in the fundamental inconsistency of quantum theory and the implications it might have on our understanding of computers, and through that, our understanding of the brain.


Professor Roger Penrose By Festival della Scienza, CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=18609251

Hamilton Lecture 2013 'Twistor Theory: A Developing Hamiltonian Legacy' Abstract

"When, in 1843, Hamilton scratched the basic equations for quaternions on the stonework of Dublin’s Broome Bridge, his brilliant algebraic representation of Euclidean 3-space initiated a role for a non-commutative algebra (ab≠ba), and a fourth dimension, into the description of physics. Through subsequent work by Clifford, Minkowski, Cartan, Heisenberg, Dirac, and many others, Hamilton’s insights were developed in numerous ways, often taking his initial innovations in unexpected directions.

One such development was the theory of twistors, initiated in 1963 as a geometric algebra for the description of physics within Minkowski’s space-time 4-geometry. Though well suited to treating massless particles and fields, twistor theory attracted little attention from the physics community until the early 21st century, when it was found useful for describing the scattering of particles at very high energies. Yet, the theory remained obstructed from its ability to address the gauge forces of particle physics and Einstein’s general relativity, by the so-called “googly problem”, which limited its applicability to left-handed rather than right-handed interactions. A recent development opens a novel route to a solution, using Hamilton’s non-commutativity in an unexpected way."

Hamilton Day 2012

The 2012 Hamilton Lecture, ‘'Silver lining, codes and clouds: Error-correcting codes, their asymptotic bounds, and Kolmogorov complexit', was delivered by ProfessorYuri Manin

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, he sketched all the relevant techniques and a proved 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.

Speaker Biography

Born 1937. M.Sc., University of Moscow 1958. Ph.D. (Candidate of physical and mathematical sciences), Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, 1960. Habilitation, Steklov Mathematical Institute, Moscow, 1963. Principal Researcher, Steklov Mathematical Institute, 1960-1993; since 1993 Principal Researcher in absentia. Professor (Algebra Chair), University of Moscow 1965-1992. Professor, M.I.T. 1992-1993. Scientific Member, MPI for Mathematics since 1993. Director, MPI for Mathematics 1995-2005, now Professor Emeritus. Board of Trustees Professor, Northwestern University (Evanston, USA) 2002-2011, now Professor Emeritus. Lenin Prize 1967. Brouwer Medal 1987. Frederic Esser Nemmers Prize 1994. Rolf Schock Prize in Mathematics 1999. King Faisal International Prize in Mathematics 2002. Georg Cantor Medal 2002. Order pour le Mérite for Science and Art, Germany, 2007. Great Cross of Merit with Star, Germany, 2008. János Bolyai International Mathematical Prize, Hungarian Academy of Sciences, 2010. Member of nine Academies of Sciences. Honorary degrees at Sorbonne, Oslo, Warwick. Honorary Member of the London Math. Society.

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