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

Preprints

Publications

1. Analysis for idempotent states on quantum permutation groups, Mathematical Physics, Analysis and Geometry - accepted

2. Tracing the orbitals of the quantum permutation group,  Arch. Math. 121, 211–224 (2023). https://doi.org/10.1007/s00013-023-01883-w (this work is subject to a correction,corrected preprint here)

3. A state-space approach to quantum permutations: Exp. Math., 2021, ISSN 0723-0869, https://doi.org/10.1016/j.exmath.2021.12.003. (earlier preprint available here).

4. The Frucht property in the quantum group setting: with Teo Banica, Glasgow Mathematical Journal, 1-31. doi:10.1017/S0017089521000380, (earlier preprint available here).

5. 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).
6. Diaconis--Shahshahani Upper Bound Lemma for Finite Quantum Groups, Fourier
   Anal Appl, 25, 2463-2491, 2019. (earlier preprint available here).
7. 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).

Regular Seminar

MIC-MTU-UCC Quantum Mathematics

Talks

1. A quantum Frucht theorem?, C*-Days in Prague, May 2023.
2. Another look at idempotent states on quantum permutation groups, Quantum Groups & Interactions Workshop, University of Glasgow, May 2023.
3. A quantum Frucht theorem?, Non-local games seminar, May 2023
4. The Kawada-Ito theorem for quantum groups, UCC BRCI mini-Symposium on Noncommutative Probability & Quantum Information, October 2022
5. The Frucht property in the quantum group setting, Quantum Group Seminar, January 2022
6. Quantum Permutations ReBorn, Quantum Group Seminar (of Teo Banica), Universite de Cergy-Pontoise, Paris.
7. Pure Mathematics: What's the Point?: The Extremely Paradoxical Extreme Utility of Pure Mathematics in Science , School of Science and Informatics Seminar, MTU.
8. The Ergodic Theorem for Random Walks: from Finite Groups, to Group Algebras, to Finite Quantum Groups, Munster Groups 2019, WIT.
9. Some Unresolved and Unexplored Aspects of Random Walks on Quantum Groups: Seminaire d'Analyse Fonctionnelle, Besancon.
10. Contexts and Concepts: A Case Study of Mathematics Assessment for Civil & Environmental Engineering, Conversations on Teaching and Learning Winter Programme 2018/19, MTU.
11. The Diaconis-Shahshahani Upper Bound Lemma for Finite Quantum Groups: Irish Mathematical Society 2018 Meeting, University College Dublin.
12. The Diaconis-Shahshahani Upper Bound Lemma for Finite Quantum Groups: Topological quantum groups and harmonic analysis Workshop, Seoul National University.
13. The Philosophy of Quantum Groups: MTU Spring Seminar Series.

Current and Recent Teaching Interests

• Civil Engineering (MATH7019, MATH7021)
• Mechanical Engineering (MATH7016)
• Biomedical Engineering & Sustainable Engineering (MATH6015, MATH6040)
• Industrial Measurement Control (MATH6037, MATH6038)
• Computing (MATH6055, MATH6000, STAT6000)
• Data Science (DATA9003, DATA8006)
• 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 (Mathematics, 2009 - 2010): Masters in Mathematics by research 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 (2004 - 2008; 2:1 awarded broken into maths (1:1) & physics (2:2)).

Other 

• I have a webpage at jpmccarthymaths.com.
• I am a keen user of Math.StackExchange, MathOverflow and MathEducators.StackExchange.