Anthony Carbery

Anthony Carbery

Anthony Carbery is currently Professor at the School of Mathematics of The University of Edinburgh. He has developed his research career as follows:

  • PhD, UCLA (1982)
  • L. E. Dickson Instructor, University of Chicago (1982-1985)
  • H. Bateman Instructor, Caltech (1983-1984)
  • Lecturer and Reader, University of Sussex (1985-1994)
  • Colin Maclaurin Professor of Mathematics, University of Edinburgh (1995)

Research field

Harmonic analysis. In particular, Tony Carbery’s research interests are around 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.

Research project

The main goals are the following:

  • To foster a common framework linking some of the areas if ICMAT’s research activity in order to develop collaborations within ICMAT, especially with its more junior members in mind.
  • To encourage a healthy inflow of external researchers and their ideas to ICMAT via the Visitors’ Programme and participation in research semesters and workshops spanning a range of themes.
  • To faciliate progress on some of the pressing questions of modern harmonic analysis.

At a mathematical level the main goals of this PVD are related to the study of:

  • Controlling Oscillation by Positivity.
  • The Structure of Linear and Multilinear Inequalites.

As a consequence, the expected results will be:

  • New concrete collaborations within ICMAT.
  • A series of internationally recognised workshops and research semesters across various themes.
  • Publication of results of research supported by ICMAT in leading international research journals.