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Department of Mathematical Sciences

The Annual Collingwood Lecture

A generous bequest has allowed the department to institute an annual lecture in memory of Sir Edward Collingwood FRS. The lectures are given by mathematicians of international renown and are suitable for a general audience. We welcome visitors from other departments and from outside the university.

Professor Pierre Cartier (Institut des Hautes Etudes Scientifiques, Paris)

"Is there a future for the cosmic Galois group?"

16 February 2017, 4.00pm, CLC013

Professor Cartier studied at the École Normale Supérieure in Paris from 1952 to 1954 and obtained his doctorate from the Université de Paris in 1958, with a thesis entitled `Derivations and Divisors in Algebraic Geometry'. By 1955, he had become a full member of the Bourbaki group (Bourbaki is the pseudonym of a group of (mainly) French mathematicians who publish an authoritative account of contemporary mathematics). He was appointed Professor in the Faculty of Science at Strasbourg in 1961, remaining there until he moved to the Institut des Hautes Études Scientifiques at Bures-sur-Yvette ten years later. In addition to this post he was director of research at the Centre National de la Recherche Scientifique from 1974. In 1982 he left the Institut des Hautes Études Scientifiques becoming a professor at the École Polytechnique (1982-88) and at the École Normale Supérieure from 1988. Professor Cartier has written papers on a broad range of mathematical topics including algebraic geometry, number theory, group theory, probability, and mathematical physics. He was awarded the Ampère Prize of the French Academy of Sciences in 1979.

Abstract: About twenty years ago, Pierre Cartier observed a similitude between the renormalization group in physics - in the construction given by Alain Connes and Dirk Kreimer - and the Grothendieck Teichmuller group in arithmetic geometry. The initial guess was a little too optimistic, based on numerical calculations by Broadhurst and Kreimer. A revised version suggests a connection between the Galois theory of transcendental numbers (as envisionned by Grothendieck) and a possible new kind of symmetry group in high energy physics: the `cosmic Galois group'. This direction has been developed by Francis Brown, giving explicit `superselection rules'. Much more is expected.




Edward Collingwood managed the family estate at Alnwick in Northumberland whilst simultaneously having a successful career as a research mathematician. He is probably known best for his work on the theory of Cluster Sets. He gave up a great deal of his time to medical administration and was, in addition, Chairman of the Council of Durham University from 1955 to his death in 1970. Collingwood College, Durham is named after him and the small research library in the department began from the nucleus of his books, collected works and journals. He was knighted in 1962, elected to the Royal Society in 1965 and became President of the London Mathematical Society in 1969.

The first Collingwood Lecture was given in 1984 by Professor Christopher Zeeman FRS on "The discovery of perspective during the Renaissance". A list of subsequent lectures is given below.

Academic Year Date Speaker Institution Title

15/16

10 May 2016

Professor Ray Goldstein

University of Cambridge

Evolution of Biological Complexity

14/15

26 Feb 2015

Professor Martin Hairer

University of Warwick

Taming Infinities

13/14

30 Jan 2014

Professor Wendelin Werner

ETH, Zurich

Randomness and the continuum

12/13

5 Nov 2013

Professor Peter Higgs, FRS

University of Edinburgh

The electroweak symmetry breaking and the Higgs boson

11/12 13 Mar 2012

Professor A. O'Hagan

University of Sheffield

Masters of Uncertainty

10/11 25 Nov 2010 Professor Robert S. MacKay, FRS University of Warwick

The Mathematics of Emergence

09/10 6 May 2010

Professor Sir John Ball, FRS

University of Oxford

Mathematics in the Public Eye: the story of Perelman and the Poincaré conjecture

08/09 7 May 2009

Professor David Spiegelhalter, FRS

University of Cambridge

Understanding Risk and Uncertainty

07/08 23 Nov 2008 Professor Vladimir Popov Steklov Institute, Moscow One and a half centuries of invariant theory
06/07 2 Mar 2007 Professor Tony Sudbery University of York Alice and Bob in the quantum wonderland
05/06 10 Mar 2006 Professor Frank Kelly

University of Cambridge

Traffic through Networks
04/05 15 Feb 2005 Professor Vladimir Turaev University of Strasbourg Curves and Words
03/04 3 Nov 2004 Professor Jon Keating University of Bristol Random Matrices and the Riemann Zeros
02/03 18 Feb 2003 Professor Don B. Zagier College de France/MPI Bonn The Experimental Side of Number Theory
01/02 9 Nov 2001 Professor GR Grimmett University of Cambridge Diffusion, Finance and Universality
99/00 11 Nov 1999 Professor NS Manton, FRS University of Cambridge Are Particles Solitons
98/99 23 Nov 1998 Sir Michael Atiyah, OM FRS University of Edinburgh The Icosahedron Past and Present
96/97 6 Dec 1996 Professor KW Morton University of Oxford Can We Trust the Numbers We Get From Our Computers
95/96 5 Dec 1995 Professor M Berry, FRS University of Bristol Quantum Mechanics, Chaos and the Prime Numbers
94/95 28 Nov 1994 Professor PJ Green University of Bristol E is MC Squared: Inference by Throwing Dice
93/94 3 Dec 1993 Dr WBR Lickorish University of Cambridge Knots in the Nineties
91/92 24 April 1992 Professor R Penrose, FRS University of Oxford Magic Dodecahedra and the Mystery of Quantum Entanglement
90/91 26 Feb 1991 Professor DV Lindley University of Warwick The Logical Analysis of Experimental Results (with Applications to Tea and Wine)
89/90 13 Mar 1990 Professor JD Barrow University of Sussex Why is the Universe Mathematical?
88/89 25 Apr 1989 Professor NH Kuiper IHES, Paris Convexity, Knots and Surfaces
87/88 14 Mar 1988 Professor D Williams, FRS University of Cambridge Probability: Philosophy and Practice
86/87 24 Feb 1987 Dr JS Bell CERN, Geneva No Action at a Distance?
85/86 13 Mar 1986 Dr PM Neumann University of Oxford The Paris Grand Prix of 1860
84/85 18 Mar 1985 Professor JH Conway, FRS University of Cambridge Cantor and the Infinite
83/84 3 May 1984 Professor EC Zeeman, FRS University of Warwick The Discovery of Perspective during the Renaissance