Gavin Brown Prize winners
The Gavin Brown Prize was established in 2011 for “an outstanding single article, monograph or book consisting of original research in Pure Mathematics”.
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 winners to date are:
- 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.