# Dr Yemon Choi

Senior Lecturer in Pure Mathematics## Research Interests

See https://www.maths.lancs.ac.uk/~choiy1/pubmath/papers.html for my papers.

### 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.

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 L^{p}(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=SL_{n}(R) or SL_{n}(Z).

## Web Links

http://www.maths.lancs.ac.uk/~choiy1/

## Professional Role

Departmental Director of Studies for students on joint degree schemes (non-LUMS)

Departmental Director of Studies for Study Abroad students

Departmental contact/representative for Natural Sciences degree programme

## PhD Supervisions Completed

Mahmood Alaghmandan, 2013. (Supervised at the University of Saskatchewan, Canada, joint with E. Samei)

Bence Horvath, 2019. (Joint with N. J. Laustsen)

Christopher Menez, 2019.

M. Eugenia Celorrio, 2023. (Joint with H. G. Dales)

## Career Details

Aug. 2022 - present: Senior Lecturer, Lancaster University, United Kingdom

Jan. 2014 - Jul. 2022: Lecturer, Lancaster University, United Kingdom

Aug. 2010 - Jan. 2014: Assistant Professor (tenure-track), University of Saskatchewan, Canada

Aug. 2008 - Jul. 2010: Postdoctoral researcher, Universite Laval, Canada

Feb. 2007 - Jul. 2008: Postdoctoral fellow, University of Manitoba, Canada

Sept. 2002 - Jun. 2006: PhD student, University of Newcastle upon Tyne, United Kingdom

Sept. 2001 - Jun, 2002: Editorial assistant, National Extension College, United Kingdom.

## Qualifications

B.A. in Mathematics (2000, Cambridge).

CASM (2001, Cambridge).

PhD in Pure Mathematics (2006, Newcastle-upon-Tyne)

## PhDs Examined

External examiner

S. Trotter (Leeds, PhD, 2016)

Y. Ji (Newcastle, PhD, 2018)

Internal examiner

E. Kastis (PhD, Lancaster, 2017)

T. Gaudio (PhD, Lancaster, 2021)

## PhD Supervision Interests

#### Availability

Subject to my existing commitments: I am always keen to hear from applicants with a strong background in functional analysis. Some previous exposure to representation theory of groups or the general theory of (matrix) Lie groups would be desirable, but is not essential.

#### Current ideas for PhD projects

Here are four possible areas in which I am willing to supervise: each of these is not a specific PhD project, but a setting in which there are various possible research problems that a student could work on. If you would like to know more, then please feel free to get in touch.

- Ulam stability for Banach and operator algebras
- Banach algebras associated to group actions on L
^{p}spaces - Fourier algebras of locally compact groups
- Non-selfadjoint subalgebras of Type I C*-algebras

#### Warning notes.

Themes 3 and 4 will require a student to start by learning the basic theory of C*-algebras, before getting on to the actual PhD project(s). C*-algebra theory is also valuable context for Themes 1 and 2, but in those cases there are "sub-projects" where one can get started on research without pre-existing C*-background.

It is possible that you are reading this and have had some exposure to various structural properties of Banach algebras known as "approximate amenability", "character amenability", or "module amenability". **I will not, for the foreseeable future, supervise on any of these three, nor on any hybrid of these.**

Selected Publications

Operators, Semigroups, Algebras and Function Theory: Volume from IWOTA Lancaster 2021

Choi, Y., Daws, M., Blower, G. 6/12/2023

Proceedings

An explicit minorant for the amenability constant of the Fourier algebra

Choi, Y. 30/11/2023 In: International Mathematics Research Notices. 2023, 22, p. 19390–19430.

Journal article

Constructing alternating 2-cocycles on Fourier algebras

Choi, Y. 16/07/2021 In: Advances in Mathematics. 385, 28 p.

Journal article

Dual convolution for the affine group of the real line

Choi, Y., Ghandehari, M. 22/05/2021 In: Complex Analysis and Operator Theory. 15, 4, 32 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

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

All Publications

Beurling-Fourier algebras and dual convolution

17/10/2022 → 28/10/2022

Research

LMS- Dr. Ebrahim Samei -Collaboration

01/08/2018 → 31/10/2018

Research

London Mathematical Society-Review & Final Approvals Travel to Delaware

25/09/2017 → 05/10/2017

Research

London Mathematical Society - Visitor Grant (Scheme 2)

01/10/2014 → 28/10/2014

Research

Internal examiner for a PhD viva (Mathematics)

Examination

Dual convolution for the affine group of the real line

Invited talk

Derivations and 2-cocycles on Fourier algebras of connected groups

Invited talk

Alternating cocycles on Fourier algebras of Lie groups

Invited talk

Amenable operator algebras: extensions and unitarizability

Invited talk

Lower bounds on the amenability constant of the Fourier algebra

Oral presentation

Unitarizability, extensions, and amenable operator algebras

Invited talk

Amenable algebras of operators on Hilbert space

Invited talk

Operator space tensor products, and cocycles on Fourier algebras

Invited talk

Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Journal)

Publication peer-review

Operator space tensor products, and cocycles on Fourier algebras

Invited talk

A twisted inclusion of operator space tensor products

Invited talk

Banach Journal of Mathematical Analysis (Journal)

Publication peer-review

Internal examiner for a PhD viva (Mathematics)

Examination

Completely almost periodic elements of group von Neumann algebras

Invited talk

Fourier algebras and dual convolution

Invited talk

An introduction to non-amenability of B(E)

Invited talk

Proceedings of the Edinburgh Mathematical Society (Journal)

Publication peer-review

Amenability constants of centres of group algebras

Invited talk

University of Delaware

Visiting an external academic institution

Constructing alternating cocycles on Fourier algebras

Invited talk

Complex Analysis and Operator Theory (Journal)

Publication peer-review

PhD viva (Mathematics) at Lancaster University (Event)

Membership of committee

Journal of Mathematical Analysis and Applications (Journal)

Publication peer-review

Alternating cocycles on Fourier algebras of Lie groups

Invited talk

Bulletin des Sciences Mathématiques (Journal)

Publication peer-review

Approximate homomorphisms: some old and new results

Invited talk

Proceedings of the American Mathematical Society (Journal)

Publication peer-review

British Mathematical Colloquium

Participation in conference -Mixed Audience

Constructing alternating cocycles on Fourier algebras

Invited talk

Jon Bannon

Hosting an academic visitor

Derivations from the disc algebra to various modules

Invited talk

Canadian Mathematical Bulletin (Journal)

Publication peer-review

Twisted tensor products, and cocycles on Fourier algebras

Invited talk

A look at Fourier algebras of some Lie groups

Invited talk

Derivations and alternating cocycles on Fourier algebras

Invited talk

External examiner for PhD viva (Newcastle)

Examination

Journal of Mathematical Analysis and Applications (Journal)

Publication peer-review

Directly finite algebras arising from group representations

Invited talk

Completely almost periodic elements of Hopf von Neumann algebras

Invited talk

Internal examiner for a PhD viva (Mathematics)

Examination

Semigroup Forum (Journal)

Publication peer-review

Some results on direct finiteness of group algebras

Invited talk

Studia Mathematica (Journal)

Publication peer-review

International Mathematical Research Notices (Journal)

Publication peer-review

External examiner for PhD viva (Leeds)

Examination

CAP and ITAP for group von Neumann algebras

Invited talk

Journal of Mathematical Analysis and Applications (Journal)

Publication peer-review

AP, WAP, CAP and another AP

Invited talk

Some operator algebras that are locally similar to self-adjoint ones

Invited talk

Derivations on Fourier algebras of connected groups

Invited talk

Indiana University Mathematics Journal (Journal)

Publication peer-review

Studia Mathematica (Journal)

Publication peer-review

Mathematical Proceedings of the Cambridge Philosophical Society (Journal)

Publication peer-review

Orthogonality relations and the study of derivations on Fourier algebras

Invited talk

Houston Journal of Mathematics (Journal)

Publication peer-review

Constructing amenable operator algebras

Invited talk

Illinois Journal of Mathematics (Journal)

Publication peer-review

Derivations on semigroup algebras and Fourier algebras

Invited talk

Canadian Journal of Mathematics (Journal)

Publication peer-review

Studia Mathematica (Journal)

Publication peer-review

The ZL-amenability constant of a finite group

Invited talk

Quarterly Journal of Mathematics (Journal)

Publication peer-review

Journal of the Australian Mathematical Society (Journal)

Publication peer-review

Orthogonality relations and the study of derivations on Fourier algebras

Invited talk

Journal of the American Mathematical Society (Journal)

Publication peer-review

Unitarizable group representations and amenable operator algebras

Invited talk

Derivations on Fourier algebras of connected Lie groups

Invited talk

Weak amenability of Fourier algebras: old and new results

Invited talk

Derivations on Fourier algebras of some connected Lie groups

Invited talk

Amenable operator algebras

Invited talk

The ZL-amenability constant of a finite group

Invited talk

Semigroup Forum (Journal)

Publication peer-review

Glasgow Mathematical Journal (Journal)

Publication peer-review

Journal of Mathematical Analysis and Applications (Journal)

Publication peer-review

Journal of Mathematical Analysis and Applications (Journal)

Publication peer-review

Journal of Mathematical Analysis and Applications (Journal)

Publication peer-review

Glasgow Mathematical Journal (Journal)

Publication peer-review

- Algebra and Geometry
- Analysis