A lecturer in the Department of Mathematics, Munster Technological University.

**Preprints**

- Tracing the orbitals of the quantum permutation group, 2023.
- Analysis for idempotent states on quantum permutation groups, 2023.

**Publications**

- A state-space approach to quantum permutations: Exp. Math., Volume 40, Issue 3

(2022), 628–664, ISSN 0723-0869, https://doi.org/10.1016/j.exmath.2021.12.003.. (earlier preprint available here). - The Frucht property in the quantum group setting: with Teo Banica, Glasgow Mathematical Journal, 1-31. doi:10.1017/S0017089521000380, (earlier preprint available here).
*The Ergodic Theorem for Random Walks on Finite Quantum Groups*,

Communications in Algebra, 49:9, 3850-3871, DOI: 10.1080/00927872.2021.1908551, 2021 (earlier preprint available here).*Diaconis–Shahshahani Upper Bound Lemma for Finite Quantum Groups,*Fourier

Anal Appl,**25**, 2463-2491, 2019. (earlier preprint available here).- The Transposition Project: Origins, Context and Early Findings: Maryna Lishchynska, Catherine Palmer, Julie Crowley, Katie Bullen, Clodagh Carroll, Patricia Cogan, David Goulding, Mark Hartnett, J.P. McCarthy, Violeta Morari, Marie Nicholson, Grainne Read, MSOR Connections, Vol 17,
**No 2**(2019)

**Talks**

- C*-days in Prague, May 2023.
- Quantum Groups & Interactions, Workshop, University of Glasgow, May 2023.
- Non-local games seminar, May 2023
- The Kawada-Ito theorem for quantum groups, UCC BRCI mini-Symposium on Noncommutative Probability & Quantum Information, October 2022,
- The Frucht property in the quantum group setting, Quantum Group Seminar, January 2022
- Quantum Permutations ReBorn, Quantum Group Seminar (of Teo Banica), Universite de

Cergy-Pontoise, Paris. - Pure Mathematics: What’s the Point?: The Extremely Paradoxical Extreme Utility

of Pure Mathematics in Science , School of Science and Informatics Seminar, MTU. - The Ergodic Theorem for Random Walks: from Finite Groups, to Group Algebras,

to Finite Quantum Groups, Munster Groups 2019, WIT. - Some Unresolved and Unexplored Aspects of Random Walks on Quantum Groups:

Seminaire d’Analyse Fonctionnelle, Besancon. - Contexts and Concepts: A Case Study of Mathematics Assessment for Civil & Environmental

Engineering, Conversations on Teaching and Learning Winter Programme 2018/19, MTU. - The Diaconis-Shahshahani Upper Bound Lemma for Finite Quantum Groups: Irish

Mathematical Society 2018 Meeting, University College Dublin. - The Diaconis-Shahshahani Upper Bound Lemma for Finite Quantum Groups:

Topological quantum groups and harmonic analysis Workshop, Seoul National University. - The Philosophy of Quantum Groups: MTU Spring Seminar Series.

**Current and Recent Teaching Interests**

– Mechanical Engineering (MATH7016)

– Civil & Environmental Engineering (MATH7019, MATH7021)

– Biomedical Engineering & Sustainable Engineering (MATH6015, MATH6040)

– Computing (MATH6055, MATH6000, STAT6000)

– Data Science (DATA9003, DATA8006)

– Industrial Measurement Control (MATH6037, MATH6038)

– Professional Diploma in Mathematics for Teachers (MB5003, MB5014, MB5021)

– Mathematical Studies in University College Cork (MS2001, MS2002, MS3011)

**Research Supervision**

- Alan Stack,
*Decision rules for abandoned football seasons,*HDip Data Science & Analytics, 2022. - Anand Prabhakar Ambujarajan,
*Methods of Smoothing Mortality Rates*, MSc Data Science & Analytics, 2020. - Tushar Kotian,
*Data Clustering for Sports Betting*, MSc Data Science & Analytics, 2020.

**Education**

- PhD, Mathematics, 2017, with Dr. Stephen Wills (UCC). The research was in Quantum Groups and the thesis title was
*Random Walks on Finite Quantum Groups — Diaconis-Shahshahani Theory for Quantum Groups*. - MSc by Research, Mathematics, 2010, with Dr. Stephen Wills (UCC). The research was in Random Walks on Finite Groups and the thesis title was
*The Cut-Off Phenomenon in Random Walks on Finite Groups*. - BSc, Joint Honours Maths & Physics, 2008, 2:1 awarded broken into maths (1:1) & physics (2:2).
- Level 9 Special Purpose Award (CIT), Effective Teaching in Higher Education, 2018.

**Other **

– I am a keen user of Math.StackExchange, MathOverflow and MathEducators.StackExchange.

** **

## 4 comments

Comments feed for this article

January 25, 2011 at 10:09 pm

jim kellyhttp://www.projectmaths.com/index.php/news-comments/

Check out the clarifications on algebra

January 25, 2011 at 10:13 pm

J.P. McCarthyJim,

These clarifications refer to Paper 1. I was wondering about Hypothesis Testing (i.e. Paper 2) – it is suspended from the syllabus. The normal distribution is still there as far as I can see but the person I was helping had never seen the tables for the normal distribution.

Regards,

J.P.

May 25, 2013 at 9:24 pm

Harold GreenHi J.P. Thank you for discovering my blog http://www.throughharoldslens.com. It gave me the opportunity to discover, explore and Follow your blog. Hope we both enjoy our journeys. Best, Harold

July 5, 2013 at 10:55 am

toorajHi, I saw your math page it was very useful , specially the c*-algebras &…(13). thanks for you.