University of Cambridge
Theoretical High Energy Particle Physics Group

Dr Alan J Macfarlane

[From the portrait by Tom Wise at St. John's College]

The picture above is from the portrait (August 2001) by Tom Wise at St. John's College

Reader in Mathematical Physics, retired 300913

Fellow of St. John's College, January 1967 to date

Research interests to 2005
Symmetries, Supersymmetry
Integrable Systems, Gaudin models, coset space models
Tensorial structures of classical Lie algebras, antisymmetric tensors, Casimir operators and related indices.
Exceptional Lie algebras: unified treatment of irreps in n-fold products of the adjoint representation, and of associated tensors

Research interests 2008-13
Compound matrices, additive compound matrices and generalisations thereof
Sequences of discrete variables used in the algebraic study of Jacobi (tridiagonal) matrices
Use of such sequences to parametrise the elements of families of matrices, e.g. those of the QD and QR algorithms
Generating functions of such sequences for the classical orthogonal polynomials, including the Jacobi polynomials

Research interests 2014-17
The geometry of the triangle centres and central lines of an arbitrary plane triangle
Use of the Steiner deltoid to motivate extending the 9-point circle to 12 point status. The Steiner deltoid is the envelope of the Simson line of a point on the circumcircle of a plane triangle as the point traverses the circle. Its points of contact with the 9-point circle yield a very interesting pattern
Integer sequences, Cellular Automata, Generating functions

For associated papers see the following

GeomTriCentsFinal.pdf or, in user/ajm/Papers2017

12PointCircleFinal.pdf or, in user/ajmPapers2017/aj in user/ajm/Papers2016 in user/ajm/Papers2016

QRQD2014.pdf or in user/ajm/Papers2015

The titles of these papers follow

On the relative distances between triangle centres lying on the central lines of an arbitrary plane triangle

On the generating functions of some integer sequences defined by the evolution of cellular automaton Rule 150

Generating functions for integer sequences defined by the evolution of cellular automata with even rule numbers

The QR algorithm and the QD algorithm applied to Jacobi matrices: parametrisation of all the elements of all their matrices using the elements of a single sequence of discrete variables.

Paper in user/ajm/Papers 2013 has title: On the compound matrices and symmetric matrix functions of a given symmetric matrix. It is not yet a final draft

The paper is in user/ajm/Papers2009. This is a longer version of the paper with the title: The Morley tricorn -- a solid figure constructed from the diagram for Morley's Theorem, which appeared in The Mathematical Gazette 95 , 49, 2011. A photograph of one of the author's models of a Morley tricorn is displayed on the front cover of number 532 of the Gazette.

Some earlier publications

Address :
Centre for Mathematical Sciences,
Wilberforce Road,
Cambridge CB3 0WA

Telephone : +44 1223 3 37874
Fax : +44 1223 7 66883

The complete set of lecture notes for O5 Electromagnetism (2002) are in user/ajm/notes.

electromagnetism O5 (.ps)

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