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Durham University

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 Gwyneth Stallard (The Open University)

"The beauty of fractals"

21 November 2018, 4.00pm, CLC013

Professor Stallard's research is in the area of complex dynamics and concerns the iteration of transcendental meromorphic functions. She has made fundamental contributions to the theory of the dynamics of transcendental complex functions and has made important discoveries concerning the dimension of Julia sets. Her insight and originality have established major results in the subject. Her work is characterised by the successful application of hard analytic techniques and, as she readily admits, by stubborness.

Gwyneth has a long standing interest in the issues surrounding women's careers in mathematics and chaired the London Mathematical Society's Women in Mathematics Committee from 2006 to 2015. This work was recognized by the award of an OBE in 2015. In 2016, she was honoured as part of the Suffrage Science Scheme, run by the Medical Research Council's Clinical Sciences Centre. She was among 12 women receiving awards in 2016 to celebrate their scientific achievements in maths and computing, and their ability to inspire others.

Abstract: In this talk we discuss the fascinating structure of geometrical objects known as fractals, beginning with classic fractal sets such as Cantor sets and the von Koch snowflake. We will then explore fractals which arise as Julia sets in the subject of complex dynamics. These are sets on which the iterates of a function behave chaotically and they have structures such as a Cantor bouquet and an infinite spider’s web. Major advances in complex dynamics have often come from applications of powerful techniques in topology and complex analysis – many of which are described in the classic text 'Collingwood and Lohwater'.

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


16 February 2017

Professor Pierre Cartier

Institut des Hautes Etudes Scientifiques

Is there a future for the cosmic Galois group?


10 May 2016

Professor Ray Goldstein

University of Cambridge

Evolution of Biological Complexity


26 Feb 2015

Professor Martin Hairer

University of Warwick

Taming Infinities


30 Jan 2014

Professor Wendelin Werner

ETH, Zurich

Randomness and the continuum


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