# Robert Wilson's Research Page

Since 2010 I have been actively involved in research in the foundations
of physics, mainly from the point of view of understanding the group
theory and representation theory of the fundamental symmetries.
The basic contradiction between quantum mechanics and general relativity
is not just a physical inconsistency, but also a mathematical one,
that manifests itself principally as an inconsistency between the
Einstein version of the Lorentz group and the Dirac version.
This in turn implies that there is an inconsistency in the definition
of mass, that propagates throughout theoretical physics.
My work is therefore aimed at providing consistent definitions of
(at least) two kinds of mass, such that the (local) equivalence
between them is a function of the type of experiment being performed.

My mathematical research is mainly in finite group theory, and related areas such
as representation theory, some aspects of combinatorics, and computational
techniques and algorithms applicable to finite groups. Some particular
aspects that interest me as listed below.
- The sporadic simple groups, especially the MONSTER, a group with

808017424794512875886459904961710757005754368000000000

elements. A recent (2010)
highlight is a construction of the Leech lattice
and Conway's group in terms of 3 by 3 octonion matrices.
- Simple constructions of exceptional groups of Lie type.
A recent (2010) highlight is the first really
elementary existence proof for the
Ree groups of type F
_{4}. A consequence of this is a construction
of the Suzuki groups which is easy enough to be presented to undergraduates.
- Algorithms for computing with matrix groups. A recent (2010)
highlight is
the publication of a paper jointly with Chris Parker, giving estimates
for the complexity of a whole range of algorithms involving involution
centralisers in groups of Lie type. This paper has been in preparation
for ten years, and the ideas in it underpin much of current algorithm
development in the area.

* This page is maintained by ***Robert Wilson**. The
views and opinions expressed in these pages are mine. The contents of
these pages have not been reviewed or approved by Queen Mary, University
of London.