We are delighted to announce that Ken Brown, Professor of Mathematics at the University of Glasgow, has been awarded the 2019 David Crighton medal by the Councils of the LMS and the IMA for his seminal contributions to noncommutative algebra and for his remarkable record of service and dedication to the UK mathematics community.
Ken has the rare ability to apply subtle ring-theoretic ideas to solve important problems in related areas. In the 1970s he solved the zero-divisor question for abelian-by-finite groups, introducing the key homological techniques which would form the basis of all later major progress in this area; according to Formanek, he made “the most important and original contribution to the problem since Higman’s  work.” In the 1980s he introduced the class of homologically homogeneous rings: in the last five years, these have been key in the study of noncommutative geometry, derived categories, and moduli spaces. His focus then shifted to the theory of quantum groups and Hopf algebra where he harnessed the combination of Hopf algebras and homological algebra to confirm important conjectures of Kac-Weisfeiler and DeConcini-Kac-Procesi in representation theory. In the last decade he has proved core results in several topics: noetherian Hopf algebras; number theory through Iwasawa algebras; Poisson geometry in Lie theory; and symplectic reflection algebras. Ken wishes to acknowledge his many collaborators in his research. He was elected a Fellow of the Royal Society of Edinburgh in 1993.
Ken has mirrored his distinguished international mathematical career with extraordinary service to the UK Mathematical Sciences community. He has a truly exceptional record of many years of tireless service on a variety of national bodies, using his positions to play an important role in fostering the vigorous state of mathematics in the UK today.
He sat on the London Mathematical Society Council for almost two decades, including terms as Vice-President from 1997-1999 and 2009-2017. During this time he was instrumental in the development of the voice of the Council for the Mathematical Sciences, providing critical input to consultations and leading a variety of task forces, particularly helping highlight the important issues that affect the Mathematical Sciences people pipeline.
Beyond this long-term involvement with the LMS, Ken has made numerous further contributions to the UK Mathematical Sciences. He was a member of the Research Assessment Exercise (RAE) Mathematics subpanel in 1996, served as Vice-Chair of this panel in 2001 and then as Chair of the RAE Pure Mathematics Subpanel in 2008. He was also a member of the Research Excellence Framework (REF) expert advisory group in 2008-09. He has been a member of the EPSRC College since 1996 and served on the EPSRC Mathematical Sciences Strategic Advisory Team (SAT) first as a member from 2013 to 2015 and subsequently as its Chair from 2015 to 2017. He was a member of the National Advisory Board of the Isaac Newton Institute (INI) from 1998 to 2002 and a member of the Scientific Committee of the International Centre for Mathematical Sciences (ICMS, Edinburgh) from 2006 till 2015. He was also a key member of the Steering Group for the International Review of Mathematics in 2010. In the Queen’s Birthday Honours List 2019, Ken was recognised with the award of Commander of the British Empire (CBE) for services to the Mathematical Sciences.
He has also been a critical figure in the development of the Mathematical Sciences in Scotland, serving the Edinburgh Mathematical Society in many roles, chairing the Glasgow Mathematical Journal Trust Fund, and acting as a spokesperson in conversations with the Scottish Funding Council which has led to pooling applications and a Scotland-wide graduate training centre.
Much of Ken’s service has been voluntary and goes far beyond his salaried responsibilities. The UK Mathematics Community would be significantly the poorer without the benefit of his selfless dedication and invaluable advice.