# Research

I work in the broad area of Functional Analysis and Operator Algebras with a particular interest in groups, group actions, and "quantum" generalisations thereof. I also have some (decreasing) interests in Data Science, see the pages on computation.

### Current activity

I am on the editorial board for the Bulletin of the Iranian Mathematical Society. To submit a paper please see the journal website.

I have acted as an editorial advisor for the Glasgow Mathematics Journal and the London Mathematical Society family of journals. My research has been supported by the EPSRC.

## Seminars

As the covid crisis continues, one silver lining has been the ability to attend virtual seminars (so I am in fact watching way more Mathematics than I usual can!). I currently attend seminars from these series:

Some older seminars which are no longer running or which I cannot attend:

## Publications

ORCID: 0000-0003-1707-4308 and arXiv.

1. "A purely infinite Cuntz-like Banach ∗-algebra with no purely infinite ultrapowers" with Bence Horváth. This paper is available on the ArXiV. Submitted
2. "Completely bounded homomorphisms of the Fourier algebra revisited". This paper is available on the ArXiV. Submitted.
3. "Ring-theoretic (in)finiteness in reduced products of Banach algebras" with Bence Horváth. Published in Can. J. Math. in press. This paper is available on the ArXiV.
4. "One-parameter isometry groups and inclusions between operator algebras". Published in New York J. Math. 27 (2021) 164--204. This paper is available on the ArXiV.
5. "Admissibility Conjecture and Kazhdan's Property (T) for quantum groups" with Biswarup Das and Pekka Salmi. Published in J. Funct. Anal. 276 (2019), no. 11, 3484--3510. This paper is available on the ArXiV.
6. "On convoluters on $L^p$-spaces" with Nico Spronk. Published in Studia Math. 245 (2019), no. 1, 15--31. This paper is available on the ArXiV.
7. "Around Property (T) for quantum groups" with Adam Skalski and Ami Viselter. Published in Comm. Math. Phys. 353 (2017), no. 1, 69--118 This paper is available on the ArXiV.
8. "Categorical aspects of quantum groups: multipliers and intrinsic groups". Published in the Canadian Journal of Mathematics volume 68 (2016), 309--333. This paper is available on the ArXiV.
9. "Non-commutative separate continuity and weakly almost periodicity for Hopf von Neumann algebras". Published in J. Funct. Anal. Volume 269 (2015) 683--704. This paper is available on the ArXiV.
10. "Quantum Eberlein compactifications and invariant means" with Biswarup Das. Published in Indiana University Mathematics Journal Vol 65 No 1 (2016) 307--352. This paper is available on the ArXiV.
11. "Remarks on the Quantum Bohr Compactification". Published in Illinois J. Math. Volume 57, Issue 4, 1131--1171. This paper is available on the ArXiV.
12. "The Haagerup property for locally compact quantum groups" with Pierre Fima, Adam Skalski and Stuart White. Published in Crelle's Journal (Journal für die reine und angewandte Mathematik) Volume 2016 Issue 711, 189--229. This paper is available on the ArXiV.
13. "Equivalence of multi-norms" with H. Garth Dales, Hung Le Pham and Paul Ramsden. Published in Dissertationes Math. Volume 498 (2014) 53pp.
14. "Completely positive definite functions and Bochner's theorem for locally compact quantum groups" with Pekka Salmi. Published in J. Funct. Anal. Volume 264, Issue 7, 1525-1546. This paper is available on the ArXiV.
15. "Closed quantum subgroups of locally compact quantum groups" with Paweł Kasprzak, Adam Skalski and Piotr Sołtan. Published in Advances in Mathematics Volume 231 (2012) 3473-3501. This paper is available on the ArXiV.
16. "Completely positive multipliers of quantum groups". Published in International Journal Mathematics volume 23, no 12 (2012). This paper is available on the ArXiV.
17. "Completely bounded representations of convolution algebras of locally compact quantum groups" with Michael Brannan and Ebrahim Samei. Published in Münster Journal of Mathematics volume 6 (2013) 445-482. This paper is available on the ArXiV.
18. "Isometries between quantum convolution algebras" with Hung Le Pham. Published in The Quarterly Journal of Mathematics 64 (2013) 373-396. This paper is available on the ArXiV.
19. "Shift invariant preduals of $\ell_1(\Z)$" with Richard Haydon, Thomas Schlumprecht and Stuart White. Published in Israel J. Math. 192 (2012), 541–585. This paper is available on the ArXiV.
20. "Multi-norms and the injectivity of $L^p(G)$" with H. Garth Dales, Hung Le Pham and Paul Ramsden. Published in J. Lond. Math. Soc. Volume 86 (2012) 779-809. This paper is available on the ArXiV.
21. "Multipliers of locally compact quantum groups via Hilbert C$^*$-modules". Published in J. Lond. Math. Soc. Volume 84 (2011) 385-407. This paper is available on the ArXiV.
22. "Multipliers, Self-Induced and Dual Banach Algebras", published in Dissertationes Mathematicae volume 470 2010, 62pp. This paper is available on the ArXiV.
23. "A bicommutant theorem for dual Banach algebras". Published in the Mathematical Proceedings of the Royal Irish Academy 111 (2011) 21-28. This paper is available on the ArXiV.
24. "Characterising weakly almost periodic functionals on the measure algebra". This paper is available on the ArXiV. published in Studia Mathematica Volume 204, 2011, 213--234.
25. "Representing multipliers of the Fourier algebra on non-commutative $L^p$ spaces", published in Canadian Journal of Mathematics Volume 63, 2011, 798--825. This paper is available on the ArXiV.
26. "Operator Biprojectivity of Compact Quantum Groups", published in Proceedings of the American Mathematical Society Volume 138, 2010, 1349-1359. This paper is available on the ArXiV.
27. "Preduals of semigroup algebras" with Hung Le Pham and Stuart White, published in Semigroup Forum Volume 80, 2010, 61--78. This paper is available on the ArXiV.
28. "Reiter's properties (P_1) and (P_2) for locally compact quantum groups", with Volker Runde, published in Journal of Mathematical Analysis and Applications Volume 364, Issue 2, 2010, 352-365. This paper is available on the ArXiV. See Corrections!.
29. "Weakly almost periodic functionals on the measure algebra", published in Mathematische Zeitschrift Volume 265 (2010) 285-296. This paper is available on the ArXiV.
30. "Conditions implying the uniqueness of the weak$^*$-topology on certain group algebras" with Hung Le Pham and Stuart White. Published in Houston Journal of Mathematics Volume 35 (number 1) 2009, 253-276. This paper is available on the ArXiV.
31. "Can B(l^p) ever be amenable?" with Volker Runde, published in Studia Mathematica Volume 188 (number 2) 2008, 151-174. See also Erratum, Studia Mathematica, Volume 195 2009, 297-298. This paper is available on the ArXiV. See Corrections!.
32. "Ultrapowers of Banach algebras and modules", published in Glasgow Mathematics Journal, Volume 50, Issue 03, 2008, 539-555. DOI:10.1017/S0017089508004400. This paper is available on the ArXiV.
33. "Amenability of ultrapowers of Banach algebras", published in Proceedings of the Edinburgh Mathematical Society, Volume 52, 2009, 307-338. DOI:10.1017/S0013091507001083. This paper is available on the ArXiV. See Corrections!.
34. "p-Operator Spaces and Figa-Talamanca-Herz Algebras", published in The Journal of Operator Theory, Volume 63, 2010, 47-83. This paper is available on the ArXiV.
35. "Arens-regularity of Algebras arising from Tensor Norms", published in the New York Journal of Mathematics Volume 13 (2007) 215-270. This is a free to access online journal.
36. "Dual Banach algebras: representations and injectivity", published in Studia Mathematica Volume 178 (number 3) 2007, 231-275. This paper is available on the ArXiV.
37. "Connes-amenability of bidual and weighted semigroup algebras", published in Mathematica Scandinavica Volume 99, Issue 2, 2006, 217-246. This paper is available on the ArXiV (warning: old version).
38. "Closed ideals in the Banach algebra of operators on classical nonseparable spaces" published in Math. Proc. Camb. Phil. Soc. Volume 140, Issue 02, March 2006, pp 317-332. DOI:10.1017/S0305004105009102. Download preprint: Acrobat PDF.
39. "Semi-simplicity of B(E)**" with Charles Read, published in Journal of Functional Analysis, Volume 219, Part 1, (2005), pp 177-204. DOI:10.1016/j.jfa.2004.04.014. Download preprint: Acrobat PDF.
40. "Arens regularity of the algebra of operators on a Banach space" published in Bulletin of the London Mathematical Society, Volume 36, Part 4, (2004), pp 493-503. DOI:10.1112/S0024609303003072. Download preprint: Acrobat PDF.

## Corrections

Some of my early papers have corrections, which can be download: corrections [PDF]. It seems I became better at checking as time went on!

## Supervision

I have had one PhD student work with me:

I was the Postdoc supervisor of Dr Biswarup Das, now a lecturer at Wroclaw University, Poland.

I have acted as the external PhD examiner for:

## MathSciNet

I have written about 50 MathSciNet reviews; if you have access, you can see the processed reviews here.

## MathOverFlow

I spend a little time on MathOverflow, although the math.FA and math.OA community is rather sparse these days.

## Thesis

My thesis was mined fairly successfully for papers (I think 6 in the end) but the original may still be of interest:

## Notes

• The group algebra derivation problem [PDF]: A self-contained proof of the group derivation problem, using the new proof by Bader et al.
• "Functorial properties of weakly almost periodic functionals on the measure algebra". This has been superseded by a later paper, as the referee noticed a much, much better way of proving the main result. However, perhaps the techniques used in this paper might be of interest: in particular, is there a non-commutative generalisation? This paper is available on the ArXiV, and will not otherwise be published (be aware that material in the first and final section is dealt with better in arXiv:0904.0436 (current version)).
• "Weakly almost periodic functionals, representations, and operator spaces": This paper shows that a completely contractive dual Banach algebra is isometric to a weak*-closed subalgebra of the algebra of completely bounded operators on a reflexive operator space. This result has been shown independently by F. Uygul (math.FA/0702200 on the arXiv), using rather similar arguments to my presentation, which will hence remain only on the arXiv.
• Bases in Banach spaces [PDF]: Introduction to Schauder bases, basic sequences, unconditional bases, and the Gowers dichotomy theorem. Prepared for a talk.
• Interpolation spaces [PDF]: Some notes on Beauzamy's book. Prepared for a talk.

### Research notes

More recently, I have been experimenting with putting LaTeX source on GitHub, where you can now find various notes: MatthewDaws/Mathematics.

## Talks

Most of my research talks.

## Conferences

For a time, I was the treasurer, and de facto secretary, of the NBFAS network. I also ran the Leeds node of the Quantum groups, operators and non-commutative probability network.

In 2010 I helped to organise a "Semester" of activities in Leeds. The website for this has been lost, but as it contained slides of talks (and I like to archive such things) I have reproduced it here: