Theoretical High Energy Particle Physics Group

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 GeomTriCentsFinal.ps, in user/ajm/Papers2017

12PointCircleFinal.pdf or 12PointCircleFinal.ps, in user/ajmPapers2017/aj

CellularAutomatonRule150.ps in user/ajm/Papers2016

GFsForCAsOfEvenRuleNo.ps in user/ajm/Papers2016

QRQD2014.pdf or QDQR2014.ps 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.

- GeomTriCentsFinal.pdf
- GeomTriCentsFinal.ps
- 12PointCircleFinal.pdf
- 12PointCircleFinal.ps
- CellularAutomatonRule150.ps
- GFsForCAsofEvenRuleNo.ps
- QRQD2014.pdf
- QRQD2014.ps
- CompoundMatricesDraft.ps
- MorleyTricorn.ps

Paper CompoundMatricesDraft.ps 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 MorleyTricorn.ps 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.

** Address : **

DAMTP,

Centre for Mathematical Sciences,

Wilberforce Road,

Cambridge CB3 0WA

E-mail:
` A.J.Macfarlane@damtp.cam.ac.uk `

** 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.

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