# Dr Yemon Choi

Lecturer in Pure Mathematics

## Research Interests

### The keyword version

Banach and operator algebras. Noncommutative harmonic analysis. Categorical and homological perspectives on functional analysis.

### The longer version

I am interested in a range of topics and problems on the interface between algebra and functional analysis. This tends to be driven by particular families of examples, but my preference is for finding general frameworks that unify common features of these examples, once one has investigated individual examples in depth. "Hacking out lots of estimates and then trying to exploit functorial behaviour" is not the most accurate description, nor the most catchy one, but it gives some idea of what I spend my research time doing.In recent years I have worked intensively on various aspects of the Fourier algebras of locally compact groups: studying these objects involves a blend of (non-commutative) harmonic analysis and representation theory. Many of the developments over the last 20 years or so use the tools, or are guided by the philosophy, of the theory of operator spaces and completely bounded maps -- these may be thought of as enriched versions of Banach spaces and linear maps between them, where one allows matricial coefficients and not just scalar ones.

I am also interested in algebras of convolution operators arising from the canonical representation(s) of a group G on the Banach space Lp(G). When p=2 there is a rich theory available, from the world of C*-algebras and von Neumann algebras; for other values of p many basic structural questions remain unresolved, even for very explicit examples such as G=SLn(R) or SLn(Z).

A gap theorem for the ZL-amenability constant of a finite group
Choi, Y. 12/2016 In: International Journal of Group Theory. 5, 4, p. 27-46. 20 p.
Journal article

Triviality of the generalized Lau product associated to a Banach algebra homomorphism
Choi, Y. 10/2016 In: Bulletin of the Australian Mathematical Society. 94, p. 286-289. 4 p.
Journal article

Realization of compact spaces as cb-Helson sets
Choi, Y. 02/2016 In: Annals of Functional Analysis. 7, 1, p. 158-169. 12 p.
Journal article

Extension of derivations, and Connes-amenability of the enveloping dual Banach algebra
Choi, Y., Samei, E., Stokke, R. 14/12/2015 In: Mathematica Scandinavica. 117, 2, p. 258-303. 46 p.
Journal article

Directly finite algebras of pseudofunctions on locally compact groups
Choi, Y. 09/2015 In: Glasgow Mathematical Journal. 57, 3, p. 693-707. 15 p.
Journal article

Weak amenability for Fourier algebras of 1-connected nilpotent Lie groups
Choi, Y., Ghandehari, M. 15/04/2015 In: Journal of Functional Analysis. 268, 8, p. 2440-2463. 24 p.
Journal article

Weak and cyclic amenability for Fourier algebras of connected Lie groups
Choi, Y., Ghandehari, M. 1/06/2014 In: Journal of Functional Analysis. 266, 11, p. 6501-6530. 30 p.
Journal article

A nonseparable amenable operator algebra which is not isomorphic to a {$C^*$}-algebra
Choi, Y., Farah, I., Ozawa, N. 10/03/2014 In: Forum of Mathematics, Sigma. 2, 12 p.
Journal article

ZL-amenability and characters for the group algebras of restricted direct products of finite groups
Alaghmandan, M., Choi, Y., Samei, E. 1/03/2014 In: Journal of Mathematical Analysis and Applications. 411, 1, p. 314-328. 15 p.
Journal article

Singly generated operator algebras satisfying weakened versions of amenability
Choi, Y. 2014 In: Algebraic methods in functional analysis. Basel : Springer Verlag p. 33-44. 12 p. ISBN: 9783034805018. Electronic ISBN: 9783034805025.
Chapter

ZL-amenability constants of finite groups with two character degrees
Alaghmandan, M., Choi, Y., Samei, E. 2014 In: Canadian Mathematical Bulletin. 57, p. 449-462. 14 p.
Journal article

Approximately multiplicative maps from weighted semilattice algebras
Choi, Y. 08/2013 In: Journal of the Australian Mathematical Society. 95, 1, p. 36-67. 32 p.
Journal article

On commutative, operator amenable subalgebras of finite von Neumann algebras
Choi, Y. 05/2013 In: Journal für die reine und angewandte Mathematik (Crelle's Journal). 678, p. 201-222. 22 p.
Journal article

Quotients of Fourier algebras, and representations which are not completely bounded
Choi, Y., Samei, E. 20/03/2013 In: Proceedings of the American Mathematical Society. 141, 7, p. 2379-2388. 10 p.
Journal article

Simplicial cohomology of band semigroup algebras
Choi, Y., Gourdeau, F., White, M.C. 08/2012 In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 142, 4, p. 715-744. 30 p.
Journal article

Characterizing derivations from the disk algebra to its dual
Choi, Y., Heath, M.J. 3/08/2011 In: Proceedings of the American Mathematical Society. 139, 3, p. 1073-1080. 8 p.
Journal article

Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras
Choi, Y., Ghahramani, F. 2011 In: The Quarterly Journal of Mathematics. 62, 1, p. 39-58. 20 p.
Journal article

Group representations with empty residual spectrum
Choi, Y. 05/2010 In: Integral Equations and Operator Theory. 67, 1, p. 95-107. 13 p.
Journal article

Simplicial cohomology of augmentation ideals in $\ell^1(G)$
Choi, Y. 02/2010 In: Proceedings of the Edinburgh Mathematical Society. 53, 1, p. 97-109. 13 p.
Journal article

Hochschild homology and cohomology of $\ell^1(\mathbb Z_+^k)$
Choi, Y. 2010 In: The Quarterly Journal of Mathematics. 61, 1, p. 1-28. 28 p.
Journal article

Injective convolution operators on $\ell^infty(\Gamma)$ are surjective
Choi, Y. 2010 In: Canadian Mathematical Bulletin. 53, 3, p. 447-452. 6 p.
Journal article

Simplicial homology of strong semilattices of Banach algebras
Choi, Y. 2010 In: Houston Journal of Mathematics. 36, 1, p. 237-260. 24 p.
Journal article

Splitting maps and norm bounds for the cyclic cohomology of biflat Banach algebras
Choi, Y. 2010 In: Banach Algebras 2009. Warsaw : Polish Academy of Sciences p. 105-121. 17 p. ISBN: 9788386806102.
Chapter

Translation-finite sets and weakly compact derivations from $\ell^1(\mathbb Z_+)$ to its dual
Choi, Y., Heath, M.J. 2010 In: Bulletin of the London Mathematical Society. 42, 3, p. 429-440. 12 p.
Journal article

Uniform bounds for point cohomology of $\ell^1(\mathbb Z_+)$ and related algebras
Choi, Y. 15/10/2009 In: Journal of Mathematical Analysis and Applications. 358, 2, p. 249-260. 12 p.
Journal article

Approximate and pseudo-amenability of various classes of Banach algebras
Choi, Y., Ghahramani, F., Zhang, Y. 15/05/2009 In: Journal of Functional Analysis. 256, 10, p. 3158-3191. 34 p.
Journal article

Biflatness of $\ell^1$-semilattice algebras
Choi, Y. 10/2007 In: Semigroup Forum. 75, 2, p. 253-271. 19 p.
Journal article

Simplicial homology and Hochschild cohomology of Banach semilattice algebras
Choi, Y. 05/2006 In: Glasgow Mathematical Journal. 48, 2, p. 231-245. 15 p.
Journal article