Tony Carbery's research interests are in classical harmonic analysis and related areas.
He is involved in the interplay of curvature with the behaviour of the operators of harmonic analysis such as the Fourier transform, oscillatory integrals and singular integrals.
More recently it has become clear that there are deep combinatorial and geometrical issues that underpin many of the problems of modern harmonic analysis. Typically, these combinatorial manifestations are easy to state but not so easy to resolve. Much of Carbery's recent research activity has been concerned with trying to highlight and push forward this perspective.
Among his former PhD students are Sarah Ziesler (now at the University of Chicago), Jon Bennett (Professor in Birmingham), Emmanuel Montini (Montreal), Sanjay Patel (Gujarat University, India), Laura Wisewell (deceased, formerly in Glasgow) and Stefan Valdimarsson (recently a postdoc at UCLA and now at the University of Iceland).
* Visitng Fellow, Isaac Newton Institute, Cambridge, January -- June 2011.
* ICM-2010 Satellite Conference in Harmonic Analysis, Bhubaneswar, India, August-September 2010, Plenary Speaker.
* CRM Pisa -- Visiting Professor April 2010
* Harmonic Analysis: International Conference on the occasion of the 60th birthday of Garcia-Cuerva and 25th anniversary of book with Rubio de Francia El Escorial (Madrid) November 17-20, 2009.
* Harmonic Analysis, Samos, Greece, September 2009.
* Harmonic Analysis and PDEs with applications, Beijing, 27 - 30 May 2009.
* Invited speaker at the 8th El Escorial Conference on Harmonic Analysis and PDE in June 2008.
* Geometric Inequalities, Banff International Research Station, Canada, 17 – 22 June 2007.
* Plenary lectures at two ICM-2006 satellite conferences in Sevilla and Barcelona.
Tony grew up in West London, studied at Oxford and then did a PhD at UCLA. After a couple of postdocs in the University of Chicago and Caltech, he returned to the UK in 1985 as a Lecturer in Mathematics at the University of Sussex. He moved to Edinburgh in 1995.
* Director, Scottish Mathematical Sciences Training Centre, (a taught course centre for PhD students in Scotland), 2007--2012. * Co-director, Centre for Mathematical Analysis and Nonlinear PDE, Maxwell Institute, 2007--2009. * Associate Editor, Journal of Geometric Analysis, 2001--2007. * Member of Management Committee (2003--2011) and Board (2003--)of ICMS. * EMS Representative on UK Council for Mathematical Sciences/EPSRC liaison group 2008 and 2009. * Specialist Adviser, Pure Mathematics, RAE 2008. *Vice-President, Edinburgh Mathematical Society, 2012--2013.