Accepted or published:

1. "Murmurations of Dirichlet characters", with K.-H. Lee, and A. Pozdnyakov, International Mathematics Research Notices, 2025(1), 2025. 

2. "Convergence of Kac--Moody Eisenstein Series over a function field", with K.-H, Lee and D. Liu, Selecta Mathematics, 31(39), 2025.

3. "Learning Fricke signs from Maass form coefficients" with J. Bieri, G. Butbaia, E. Costa, A. Deines, K.-H. Lee, D. Lowry-Duda, Y. Qi, T. Veenstra, to appear in Advances in Theoretical and Mathematical Physics.

4. "Murmurations of elliptic curves", with Y.-H. He, K.-H. Lee, and A. Pozdnyakov, to appear in Experimental Mathematics. 

5. "PCA, arithmetic, and murmurations", International Journal of Data Science in the Mathematical Sciences, 2(2), 89-97, 2024.

6. "Machine learning for number theory: unsupervised learning with L-functions", Lecture Notes in Computer Science, 14749, 196-203, 2024. 

7. "Machine learning the invariants of arithmetic curves", with Y.-H. He and K.-H. Lee, Journal of Symbolic computation, 115, 478-491, 2023.

8. "Machine Learning Class Numbers of Real Quadratic Fields", with M. Amir, Y.-H. He, K.-H. Lee, and E. Sultanow, International Journal of Data Science in the Mathematical Sciences, 1(2), 107-134, 2023.

9. "Machine-learning number fields", with Y.-H. He and K.-H. Lee, Mathematics, Computation and Geometry of Data, 2, 49-66, 2022.

10. "Ratios of Artin L-functions", with L. Hochfilzer, Journal of Number Theory, 236, 1-40, 2022.

11. "Machine-learning the Sato-Tate conjecture", with Y.-H. He and K.-H. Lee, Journal of Symbolic Computation, 111, 61-72, 2022.

12. "Character expansion of Kac-Moody correction factors", with K.-H. Lee and D. Liu, Pacific Journal of Mathematics, 313(1), 159-183, 2021.

13. "Weil's converse theorem for Maass forms and cancellation of zeros", with M. Neururer, Acta Arithmetica, 196(4), 387-422, 2020.

14. "Twisting moduli for GL(2)", with B. Bedert, G. Cooper and P. Zhang, Journal of Number Theory, 217:142-162, 2020.

15. "A conjectural extension of Hecke's converse theorem", with S. Bettin, J. W. Bober, A. R. Booker, B. Conrey, M. Lee, G. Molteni, D. J. Platt, R. S. Steiner, The Ramanujan Journal, 47(3), pp 659-684, 2018.

16. "Mean-periodicity and automorphicity", Journal of the Mathematical Society of Japan, volume 69(1):25-51, 2017.

17. "Zeta integrals on arithmetic surfaces", Algebra i Analiz, 27(6): 199-233, 2015; reprinted in St. Petersburg Mathematical Journal, 27(6): 1003-1028, 2016.

Preprints:

18. "Machine learning the vanishing order of rational L-functions" with J. Bieri, G. Butbaia, E. Costa, A. Deines, K.-H. Lee, D. Lowry-Duda, Y. Qi, T. Veenstra, arXiv:2502.10360.

19. "Divisibility rules for integers presented as permutations", with A. Vernitski, arXiv:2502.15559.

20. "AI-assisted mathematical discovery: a new pattern in the primes", with Y.-H. He, K.-H. Lee and A. Pozdnyakov, submitted.

Book chapters:

21. "Supervised learning of arithmetic invariants", in Machine Learning in Pure Mathematics and Theoretical Physics, World Scientific, 331-363, 2023.

22. "Notes on low degree L-data", in Analytic Number Theory and Related Areas, RIMS Kôkyûroku, 2014:48 -58, 2017.

Other:

22. "Counting points on elliptic curves", with C. Wuthrich, LMS Newsletter, 509: 31-35, 2023.

23. "Why OpenAI developing an artificial intelligence that's good at maths is such a big deal", The Conversation, 04 December 2023.

• AI meets mathematics, Imperial, Aug 2025.

• Machine learning and mathematics, KIAS, July 2025.

• NTAG seminar, Exeter, Feb 2025.

• Strings online Lisbon, Nov 2024.

• Arithmetic study group, Durham, Oct 2024.

• International congress on mathematical software, Jul 2024.

• Jean Monnet Université Saint-Étienne, Mar 2024.

• Hybrid conference on AI-Math, Feb 2024.

• University of Cambridge, Feb 2024.

• University of Greenwich, Nov 2023.

• Isaac Newton Institute, Oct 2023.

• ICERM, Jul 2023.

• London Institute for Mathematical Sciences, Jul 2023.

• London algebra colloquium, Queen Mary, Nov 2022.

• Arithmetic study group, Durham, Nov 2022.

• Heilbronn seminar, Bristol, June 2022.

• Maths club, Teesside, March 2022.

• Undergraduate Research Seminar, Nottingham, Nov 2021.

• Online machine learning seminar, Sept 2021.

• University of Sheffield, Aug 2021.

• International seminar on automorphic forms, Jan 2021.

• "North meets south" colloquium, Oxford, Mar 2020.

• University of Warwick, Jan 2020.

• University of Nottingham, May 2019.

• University of Oxford, Feb 2019.

• Durham University, Feb 2019.

• Brown University, Nov 2018.

• Yale University, Nov 2018.

• University of Connecticut, Nov 2018.

• University of Bristol, Nov 2017.

• ​Freie Universitat Berlin, May 2017.

• University of Connecticut, Apr 2017.

• Université Lille 1, Mar 2017.

• University of Exeter, Jan 2017.

• British Mathematical Colloquium, Mar 2016.

• University of Warwick, Mar 2015.

• University of Nottingham, Dec 2015.

• University of Nagoya, Nov 2015.

• RIMS Kyoto, Nov 2015.

• University of Bristol, Jan 2014.

• Durham University, Feb 2014.

• Warwick-Nottingham-Durham-Sheffield joint seminar, May 2014.

• University of Sheffield, Feb 2013.

• Independent University of Moscow, Sep 2013.

• ​Independent University of Moscow, Nov 2012.