Ryan O'Loughlin

Ryan O'Loughlin


I am a fourth-year PhD student in the Analysis department, supervised by Professor Jonathan Partington. I am working in the field of Functional Analysis.

Research interests

I am interested in the field of Operator Theory - in particular:

  • Toeplitz operators
  • Truncated Toeplitz operators
  • Model spaces
  • Nearly invariant subspaces

Publications and preprints:

  • Toeplitz kernels and the backward shift; (2020) Ryan O’Loughlin; Journal of Mathematical Analysis and Applications. A copy is available at https://doi.org/10.1016/j.jmaa.2020.124489
  • Nearly invariant subspaces with applications to truncated Toeplitz operators; (2020) Ryan O’Loughlin; Complex Analysis and Operator Theory. A copy is available at https://doi.org/10.1007/s11785-020-01049-4
  • Matrix-valued truncated Toeplitz operators: unbounded symbols, kernels and equivalence after extension; (2020) Ryan O’Loughlin. A preprint is available on my arxiv page, http://arxiv.org/a/oloughlinr1
  • Truncated Toeplitz operators on multiband spaces; (2020) M. Cristina Câmara, Ryan O’Loughlin, Jonathan R. Partington. A preprint is available on my arxiv page, http://arxiv.org/a/oloughlinr1


  • “The Kernel of a Toeplitz Operator” – University of Leeds pure PG seminar 2018
  • “Minimal Kernels and Maximal Functions” – University of Paris-Est Marne-la-Vallée, ACOTCA 2019
  • “Resolvent Estimates and the Spectral Measure: The Mourre estimate” – Analysis commutator methods reading group, University of Leeds 2019
  • “An Introduction to the Invariant Subspace Problem” – University of Leeds pure PG seminar 2019
  • “Functional Calculus for Sectorial Operators” – Analysis reading group, University of Leeds 2020
  • Newcastle University analysis seminar – Postponed due to the coronavirus pandemic.

Organised events

I was the sole organiser of the Young Functional Analysts’ Workshop 2019, held at the University of Leeds. More information on the meeting can be found at Young Functional Analysts' Workshop (google.com).


I have taught the following courses at the University of Bath:

  • Analysis 1 (semester 1) 2015-2016, 2016-2017
  • Analysis 1 (semester 2) 2015-2016, 2016-2017

Each of these involved marking students work and giving a weekly hour long tutorial.

I have taught the following courses at the University of Leeds:

  • Sets, Sequences and Series 2017-2018, 2018-2019, 2019-2020
  • Introduction to Geometry 2019-2020
  • Linear Algebra with Applications 2018-2019

My role as tutor for these courses was to lead an example class each week and give feedback on a weekly or biweekly problem sheet.

During the summer of 2017 I taught English at Humen Foreign Languages School in Dongguan, China.

Taught courses attended

I have attended the following magic courses. See MAGIC Maths (maths-magic.ac.uk) for course details.

  • Mathematical Methods 2017 – 2018
  • Banach spaces and Fredholm theory 2017 – 2018
  • Spectral Theory of Ordinary Differential Operators 2017 – 2018
  • Theory of Partial Differential Equations 2017 – 2018
  • Functional Analysis 2017 – 2018
  • Banach spaces of analytic functions 2017 – 2018
  • Classical Wavelet Theory 2018 – 2019
  • Operator Algebras 2019 – 2020


  • EPSRC grant awarded for PhD studies
  • University of Bath scholarship, 2013-2014, 2014-2015, 2015-2016, 2016-2017
  • In the summer of 2016 I was awarded a University of Bath IMI grant for a project focused on the Fourier Analysis of groups. This project was under the supervision of Dr Veronique Fischer-Home Page for Veronique Fischer (bath.ac.uk)


  • Mmath (University of Bath) - First class