Gus Lehrer solves a 75-yr-old mathematical question

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The Australian Academy of Science has honoured University of Sydney academic Professor Gustav Lehrer from the School of Mathematics and Statistics who among other achievements solved a 75-yr-old mathematical problem.

Professor Gus Lehrer

Each year the Academy presents awards to recognise scientific excellence in research.

Professor Gustav Lehrer was awarded the Hannan Medal for his highly influential contributions to algebra and geometry.

Highlights include his co-invention of the theory of cellular algebras in the decade’s most highly cited Australian mathematical work. These are mathematical structures designed to encode how simple geometric diagrams can be combined to produce more complicated ones. By this means it is possible to analyse diagrams algebraically. Examples include diagrams of chromosomes knotted with each other, or the diagrams formed by traces of paths of atomic or subatomic particles moving around.

He also developed ‘Howlett-Lehrer theory’ to solve decomposition problems in algebra and geometry; these problems use the fact that certain algebraic structures have a great deal of symmetry, and this symmetry may be used to analyse them by decomposing them into simpler structures. In addition, he coinvented ‘Springer-Lehrer theory’ for the study of kaleidoscopic reflections. This analysis studies the type of geometry one obtains by putting many mirrors together and studying the resulting images. It is crucial in understanding what types of symmetry can actually occur in nature.

His recent joint solution of the second fundamental problem of invariant theory resolved a mathematical question of 75 years standing. This problem involved determining how quantities which are invariant (unchanged) under certain geometric transformations, depend on each other.

The Hannan medal is awarded for research in pure mathematics every 6 years.

Gus Lehrer is president of the Sydney Jewish Museum.