The Gavin Brown Prize was established in 2011 for an outstanding and innovative piece of research in the mathematical sciences published by a member or members of the Society.

The Gavin Brown Prize will awarded annually at the annual meeting of the AustMS.
Find out more here about background and rules of the Prize.

Gavin Brown Prize winning papers to date are:

• 2019 — Zdravko Botev, Joseph Grotowski and Dirk Kroese Kernel Density Estimation via Diffusion, The Annals of Statistics, Vol. 38, No. 5, (2010) 2916–2957
  
  This work has been described as ‘stunning’, ‘exceptionally well written’ and ‘extraordinary’. Marrying ideas from mathematical analysis and applied statistics, the trio have been praised for their fast kernel density estimator, which also achieves excellent accuracy thanks to an ingenious bandwidth selection algorithm.
  This work is yet another example of the unifying power of mathematics — our estimator uses the abstract concepts originally due to Fourier, Einstein and others, that describe phenomena ranging from the spread of heat in objects through to the spread of information in social networks.
• 2018 — Nicholas R. Beaton, Mireille Bousquet-Mélou, Jan de Gier, Hugo Duminil-Copin, Anthony J. Guttmann The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+√2, Comm. Math. Phys. 326 (2014), 727–754
  
• 2016 — Professor George Willis and Professor Yehuda Shalom^* (Israel)Commensurated Subgroups of Arithmetic Groups, Totally Disconnected Groups and Adelic Rigidity, Geometric and Functional Analysis, Vol. 23, 1631–1683 (2013)
  
  The paper is notable for a number of reasons. The authors answer the conjecture of Margulis and Zimmer for a broad class of groups, roughly speaking for groups commensurable with G(O), where G is a Chevalley group over a global field K of characteristic zero, and O is the ring of integers of K. The methods they use are novel, imposing a topology in such a way that they are able to draw on results from the study of general totally disconnected groups. Finally, they provide a unified framework for considering a number of results and conjectures in the rigidity theory of arithmetic groups. A number of experts consider that this final contribution may perhaps become the strongest legacy of the paper.
  
  ^*Yehuda Shalom is not eligible to receive the Gavin Brown Prize, as he has not been a member of AustMS during the last 10 years.
• 2015 — Professor Andrew Hassell Ergodic billiards that are not quantum unique ergodic, Annals of Mathematics 171:2 (2010), 605–619.
• 2014 — Professor Ben Andrews and Dr Julie Clutterbuck Proof of the fundamental gap conjecture, J. Amer. Math. Soc. 24 (2011), 899–916.
  
• 2011 — Professor Neil Trudinger FAA, FRS, FAustMS and Professor Xu-Jia Wang FAA, FAustMS Xi-Nan Ma^* (ECNU), Neil S. Trudinger (ANU), Xu-Jia Wang (ANU)
  Regularity of Potential Functions of the Optimal Transportation Problem
  Archive for Rational Mechanics and Analysis, 177 (2005), no. 2, 151–183.
  
  The paper unlocked a problem mentioned in the Fields medallist Cedric Villani's 2003 AMS book on optimal transport as "the most important" remaining to be understood in the area of smoothness of optimal transport, namely the regularity in a geometric (Riemannian) setting. The problem seemed to be monstrously difficult and Caffarelli apparently thought it to be intractable. Then arrived Ma, Trudinger and Wang, and their discovery (by brute analytic force) of what is now called the "Ma–Trudinger–Wang tensor". The paper was like a lightning strike, and was the start of a new direction of research stimulating many papers and it was their contribution that made all this possible, a remarkable insight both in the theory of optimal transport and in differential geometry.
  ^*Xi-Nan Ma is not eligible to receive the Gavin Brown Prize, as he has not been a member of AustMS during the last 10 years.