## Maths stars shine in Australian Academy of Science awards

**8 December 2014**

The Australian Academy of Science has honoured both early career and life-long achievement with awards to two University of Sydney academics in theSchool of Mathematics and Statistics.

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 and used to analyse diagrams algebraically.

He also developed the 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 which can be used to analyse them by 'decomposing' them into simpler structures.

In addition, he co-invented 'Springer-Lehrer theory' for the study of kaleidoscopic reflections. The theory analyses the type of geometry obtained by putting many mirrors together and studying the resulting images.

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 unchanged under certain geometric transformations depend on each other.

Professor Alan McIntosh from the Mathematical Sciences Institute at the Australian National University was also awarded the Hannan medal, which is awarded for research in pure mathematics every six years.

For early career achievement Associate Professor Jean Yang was awarded the Academy's Moran medal.

Associate ProfessorYang is an applied statistician who has made significant contributions to the development of statistical methodology for analysing molecular data arising in contemporary biomedical research.

Her work on removing extraneous variability from certain data has been incorporated in major software packages used worldwide to identify gene expression patterns.

She has also developed novel methods for integrating molecular and clinical data and has already made an impact on melanoma research by identifying potential genes that help with predicting survival outcome.

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