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MGP entry | academic history | MathOverflow profile

Curriculum vitae in PDF format (A4 page size); this file last updated April 2021.

Currently I am Treasurer of the North British Functional Analysis Seminar (NBFAS), having previously acted as the Lancaster representative from 2014-18. The current Secretary is Dr. E. Kakariadis (Newcastle).

Research

The end of all our exploring
Will be to arrive where we started
And know the place for the first time

Broadly speaking, I study algebraic structures that arise in functional analysis. In the initial ("pre-permanent") part of my career, this mainly meant considering homological phenomena — lifting problems, extension problems, and (co)homological invariants — for Banach algebras and their modules. Underlying many of these phenomena and questions is the concept of amenability for Banach algebras, introduced in the 1970s by B. E. Johnson, although my PhD was really aimed at finding out what could be said for non-amenable examples that had some residual "good behaviour" of their Hochschild cohomology groups.

Since 2010 my emphasis has shifted towards topics and examples that arise in abstract harmonic analysis, such as the structural properties and representation theory of (semi)group algebras, algebras of convolution operators, and Fourier algebras. From 2011-2014 this work was partly supported by the research grant NSERC 402153-2011.

For a better idea of what this has meant in practice, see my list of papers. See also:

which were all intended to have the flavour of a survey of results by various people, together with my own contributions.

Currently (2020-21) I have returned, after a few years' unintended hiatus, to the study of Fourier algebras on Lie groups and particular classes of discrete groups, although there are still some collaborative projects concerning certain algebras of operators on $L^p$-spaces that are in the writing-up stage.

Despite the specialized terminology above, I see myself as a generalist rather than a specialist, and am not a fan of tribal distinctions between particular areas of pure mathematics, nor of occasional outbreaks of mathematical absolutism that I see online which proselytize "the right way to do things".

Conference/session organization

In 2019, I was joint organizer (with D. Kitson and M. Daws) of the Analysis session of the British Mathematical Colloquium at Lancaster.

In 2016, I was local organizer for a meeting of NBFAS in Lancaster. The speakers were M. Kennedy (Waterloo) and C. Anantharaman-Delaroche (Orléans).

In 2012, I was joint organizer (with E. Samei) of the session Harmonic Analysis and Operator Spaces at the summer meeting of the Candian Mathematical Society, held in Regina.

Editorial, review, and referee work

My CV includes some of the journals for whom I have done refereeing work. I am also currently a reviewer for the AMS's Mathematical Reviews® database: see here for the processed reviews to date.

I was joint editor with N. J. Young of

Surveys in Contemporary Mathematics.
LMS Lecture Notes 347, Cambridge University Press, 2008 [Math Reviews]

This volume is a sequel of sorts to

Surveys in Geometry and Number Theory.
LMS Lecture Notes 338, Cambridge University Press, 2007 [Math Reviews]

for which I did the TeXnical editing.

Notes and jottings

Stopgap page linking to personal webpages of some departmental colleagues.

Some people with Google Scholar pages

Links for analysis on the Heisenberg group(s)

Linked here for my own convenience: handwritten note on the left and right M(G)-actions on various modules.

During my PhD (2002-06) I made a few attempts at writing up expository material -- these haven't been updated since, but I may yet get back to re-organizing or re-working the material.

On and off over the last few years, I have attempted to contribute to the n-Lab pages on topics related to Banach algebras (usually just to correct some breezy or wrong claims by people who are cavalier, but also to get my own preconceptions/misconceptions challenged and corrected).

Out-of-date stuff

There is a (temporary) page of general maths links, which hasn't been updated for several years now. A mixed bag of unsorted links has been moved to a separate page for the moment.