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2020 Hector Medal: the algebra of algorithms

Professor Eamonn O’Brien FRSNZ has been awarded the Hector Medal by Royal Society Te Apārangi for his outstanding and internationally recognised contributions to the mathematical sciences.

Eamonn is a world leading expert in the development of highly effective algorithms for group theory.  These algorithms are now incorporated into the computer algebra systems GAP and MAGMA that allow mathematicians world-wide to access these cutting-edge computational research tools.

His research contributions are many and varied. Major highlights of his research include the solution in his PhD thesis of a 1940s challenge problem posed by Alan Turing, classifying the groups of order 256. His work on this topic culminated in the classification of the groups of order at most 2000, as reported in Nature in 2000. Other highlights include his role in developing the only known efficient algorithm to construct random elements of finite groups, and the proof of the long-standing Ore Conjecture.  He is also a leader of the highly influential “Matrix Group Recognition” project, which drove workshops in Germany in 2011 and 2019.

Eamonn is author of a highly cited research monograph, and has published 85 refereed articles in leading international journals including Inventiones Mathematicae, Journal of the European Mathematical Society, and Transactions of the American Mathematical Society. He is one of the most highly-cited mathematical researchers in New Zealand.

He has given many invited plenary lectures at major international meetings and his research has attracted significant funding, including a Humboldt Foundation Fellowship, eight Marsden Fund awards (continuously since 1998), and a €300,000 research programme at the Hausdorff Institute (Bonn). He held a Maclaurin Fellowship 2007-2008, and a Hood Fellowship in 2016.

Eamonn's professional service is also impressive. In addition to serving on several evaluation panels, he is Managing Editor for the Computational Section of the Journal of Algebra, and is currently President of the New Zealand Association of Humboldt Fellows.

Eamonn is a Professor of Mathematics at University of Auckland.  His research leadership has fostered the University of Auckland as a strong research centre for Algebra. He won the New Zealand Mathematical Society's annual Research Award in 2004, and was elected a Fellow of the Royal Society of New Zealand in 2009.  

On receiving the Hector Medal, Eamonn said: “I am honoured to receive the Hector Medal and thank Royal Society Te Apārangi for this award. Over my entire career, I have been supported by many colleagues, both in New Zealand and overseas, and acknowledge the critical roles they have played in my achievements. I am particularly grateful to my long-time collaborators at the University of Auckland, Jianbei An and Marston Conder. I also thank my partner Alistair and my family for their continuous support and encouragement."


Hector Medal:
For outstanding work in chemical, physical sciences, or mathematical and information sciences.

To Eamonn Anthony O'Brien for the development of highly effective algorithms for group theory, widely used in computational algebra systems, and their application to answer major long-standing research problems.