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 QR algorithm
Generating functions of such sequences for the classical orthogonal polynomials, including the Jacobi polynomials

Research interests 2014-16
The geometry of the triangle centres and central lines of an arbitrary plane triangle
Umbral calculus, Bell and Stirling numbers, Bell and Charlier polynomials
Integer sequences, Cellular Automata, Generating functions

A paper on the first of these areas may be seen as GeomTriCents.pdf or in user/ajm/Papers2015

One on the second: BellFibo2014.pdf which has the title: Bell polynomials and Fibonacci numbers

Two on the third: in Papers2016

and: also in Papers2016

The titles of the two recent entries are

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

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

Also in Papers2015 is a paper with the title: 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. See QRQD2014.pdf or

There were (January 2013) two papers in user/ajm/Papers2013. The first paper Paper2013a has been supressed and replaced (January 2015) by the paper QRQD2014.pdf or .ps in Papers2015. Paper2013b 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.

Papers 2009