Publications

1. Nils Bruin, Nathan Ilten, Zhe Xu, Local Euler characteristics of A_n-singularities and their application to hyperbolicity, ArXiv preprint arXiv:2312.01722 (2023). See also Electronic resources.
2. Nils Bruin, Avinash Kulkarni, On (2,2)-decomposable genus 4 Jacobians, ArXiv preprint arXiv:2309.01959 (2023). See also Electronic resources.
3. Nils Bruin, E. Victor Flynn, Ari Shnidman, Genus two curves with full sqrt(3)-level structure and Tate-Shafarevich groups, Selecta Mathematica 29, 42 (2023). (or see ArXiv preprint arXiv:2102.04319).
4. Nils Bruin, Jordan Thomas, Anthony Várilly-Alvarado, Explicit computation of symmetric differentials and its application to quasi-hyperbolicity, Algebra and Number Theory 16 no. 6 (2022), 1377-1405. (or see ArXiv preprint arXiv:1912.08908).
5. Nils Bruin, Eugene Filatov, Twists of the Burkhardt Quartic Threefold, Research in Number Theory 9, 73 (2022). (or see ArXiv preprint arXiv:2207.04393, 2022).
6. Nils Bruin, Linden Disney-Hogg, Wuqian Effie Gao, Rigorous numerical integration of algebraic functions, ArXiv preprint arXiv:2208.12377 (2022).
7. Nils Bruin, Daniel Lewis, Two-cover descent on plane quartics with rational bitangents, ANTS XIV: Proceedings of the Fourteenth Algorithmic Number Theory Symposium, The Open Book Series 4-1 (2020), 73-89. See also Electronic resources. (or see ArXiv preprint arXiv:2003.00666). Conference Video Presentation (also on YouTube) and the slides.
8. Nils Bruin, Emre Can Sertöz, Prym varieties of genus four curves, Trans. AMS 373 (2020), 149-183. Electronically published on September 23, 2019. (or see ArXiv preprint arXiv:1808.07881, 2018).
9. Nils Bruin, Jeroen Sijsling, Alexandre Zotine, Numerical computation of endomorphism rings, ANTS XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium, The Open Book Series 2-1 (2019), 155-171. See also Electronic Resources. (or see ArXiv preprint arXiv:1807.02605, 2018).
10. Nils Bruin, Brett Nasserden, Arithmetic aspects of the Burkhardt quartic threefold, J. London Math. Soc. 98 (2018), 536 - 556. See also Electronic Resources (or see ArXiv preprint arXiv:1705.09006)
11. Nils Bruin, Tom Fisher, Visibility of 4-covers of elliptic curves, Research in Number Theory 4:11 (2018) (or see ArXiv preprint arXiv:1701.07528,, 2017).
12. Nils Bruin, Bjorn Poonen, Michael Stoll, Generalized explicit descent and its application to curves of genus 3, Forum Math. Sigma 4 (2016), e6, 80 pp.
13. Nils Bruin, E.Victor Flynn, Damiano Testa, Descent via (3,3)-isogeny on Jacobians of genus 2 curves, Acta Arithmetica 165 (2014), 201-223. (or see ArXiv preprint arXiv:1401.0580, 2014).
14. Nils Bruin, Success and challenges in determining the rational points on curves, ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium, The Open Book Series 1-1 (2013), 187-212.
15. Nils Bruin, Brett Hemenway, On congruent primes and class numbers of imaginary quadratic fields, Acta Arithmetica 159 (2013), 63-87. (or see ArXiv preprint arXiv:1110.5959, 2011).
16. Nils Bruin, Alexander Molnar, Minimal models for rational functions in a dynamical setting, LMS Journal of Computation and Mathematics, 15 (2012), 400-417. See also Electronic Resources (or see ArXiv preprint arXiv:1204.4967, 2012).
17. Jason P. Bell, Nils Bruin, Michael Coons, Transcendence of generating functions whose coefficients are multiplicative, Trans. Amer. Math. Soc. 364 (2012), 933-959 (or see ArXiv preprint arXiv:1003.2221, 2010).
18. Nils Bruin, Kevin Doerksen, The arithmetic of genus two curves with (4,4)-split Jacobians, Canad. J. Math. 63 (2011), 992-1021. See also Electronic Resources (or see ArXiv preprint arXiv:0902.3480, 2009).
19. Nils Bruin, Michael Stoll, The Mordell-Weil sieve: Proving non-existence of rational points on curves, LMS Journal of Computation and Mathematics 13 (2010), 272-306. (or see ArXiv preprint arXiv:0906.1934, 2009).
20. Nils Bruin, Sander R. Dahmen, Visualizing elements of Sha[3] in genus 2 jacobians, Algorithmic Number Theory, 9th International Symposium, ANTS-IX, Lecture Notes in Computer Science 6197, Springer 2010, pp. 110 - 125, (ArXiv preprint arXiv:1001.5302, 2010.)
21. Nils Bruin, Michael Stoll, Two-cover descent on hyperelliptic Curves, Math. Comp. 78 (2009), 2347-2370. See also Electronic Resources. (or see ArXiv preprint arXiv:0803.2052, 2008)
22. Nils Bruin and Michael Stoll, Deciding existence of rational points on curves: an experiment, Experiment. Math. 17 (2008), no. 2, 181-189. See Electronic data for additional resources. (or see arXiv preprint, 2006).
23. Nils Bruin, The arithmetic of Prym varieties in genus 3, Compositio Mathematica (2008), 144 : 317-338. See Electronic Data for supporting electronic resources. (or see arXiv preprint, 2004).
24. Bright, M. J.; Bruin, N.; Flynn, E. V.; Logan, A. The Brauer-Manin obstruction and Sha[2], LMS J. Comput. Math. 10 (2007), 354--377. Electronic resources available in Appendix A or here.
25. Nils Bruin, Julio Fernández, Josep González, Joan-Carles Lario, Rational points on twists of X₀(63), Acta Arith. 126 (2007), no. 4, 361-385. Also available as Preprint at Universitat Politecnica Catalunya.
26. Nils Bruin, K. Györy, L. Hajdu, Sz. Tengely, Arithmetic progressions consisting of unlike powers, Indag. Mathem. 17 (4), 539-555 (2006). Also available as preprint.
27. Nils Bruin, E. Victor Flynn, Josep González, Victor Rotger, On finiteness conjectures for endomorphism algebras of abelian surfaces , Math. Proc. Camb. Phil. Soc. (2006) 141, 383-408. (or see arXiv preprint). See Electronic Data for supporting electronic resources.
28. Michael A. Bennett, Nils Bruin, Kálmán Györy, Lajos Hajdu, Powers from Products of Consecutive Terms in Arithmetic Progression, Proc. London Math. Soc. (3) 92 (2006), no. 2, 273 - 306.
29. Nils Bruin, E. Victor Flynn, Exhibiting Sha[2] on Hyperelliptic Jacobians, Journal of Number Theory, 118 (2006), pp. 266-291.
30. Nils Bruin, The primitive solutions to x^3+y^9=z^2, Journal of Number Theory, 111 (2005), pp. 179-189. (Or see arXiv preprint, 2003). See Transcript of computations for supporting electronic resources.
31. Nils Bruin and E. Victor Flynn, Towers of 2-covers of hyperelliptic curves, Trans. Amer. Math. Soc. 357 (2005), 4329-4347. (or see Towers of 2-covers of hyperelliptic curves, Preprint PIMS-01-12, 2001)
32. Nils Bruin and E. Victor Flynn, Rational Divisors in Rational Divisor Classes, in Duncan Buell (Ed.): Algorithmic Number Theory, 6th International Symposium, ANTS-VI, Lecture Notes in Computer Science 3076 Springer 2004, pp. 132 - 139.
33. Nils Bruin, Visualisation of Sha[2] in Abelian Surfaces, Math. Comp. 73 (2004), no. 247, 1459 - 1476. See Electronic Data for supporting electronic resources.(or see arXiv preprint, 2002).
34. Nils Bruin, Some ternary Diophantine equations of signature (n,n,2), in Discovering Mathematics with Magma, W. Bosma, J. Cannon (eds). Algorithms Comput. Math., 19, Springer, Berlin, 2006, pp. 63-91. See Electronic Data for supporting electronic resources.
35. Nils Bruin, Chabauty methods using elliptic curves. J. Reine Angew. Math. 562 (2003), 27 - 49. (it seems the 2003 volumes of Crelle have fallen of the map, so as a stop-gap measure a cached copy. No copyright infringement intended)
36. N.R. Bruin, Chabauty methods and covering techniques applied to generalized Fermat equations, CWI Tract 133, 77 pages, 2002.
37. Nils Bruin and Noam D. Elkies, Trinomials ax^7+bx+c and ax^8+bx+c with Galois Groups of Order 168 and 8*168, in Claus Fieker, David R. Kohel (Eds.): Algorithmic Number Theory, 5th International Symposium, ANTS-V, Lecture Notes in Computer Science 2369 Springer 2002, pp. 172 - 188.
38. Nils Bruin and E. Victor Flynn, N-Covers of hyperelliptic curves, Math. Proc. Cambridge Philos. Soc. 134 (2003), no. 3, 397--405.
39. Nils Bruin, On powers as sums of two cubes, in Wieb Bosma (ed.),Algorithmic Number Theory 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000 Proceedings. Springer LNCS 1838. Associated files: prf335.g, tor334.mpl, prf335.mpl.
40. Nils Bruin, Chabauty methods and covering techniques applied to generalised Fermat equations, PhD-thesis, University of Leiden, 1999. errata. Also the accompanying stellingen (in dutch). (pdf version)
41. Nils Bruin, The diophantine equations x^2+-y^4=+-z^6 and x^2+y^8=z^3, Compositio Math. 118 (1999) 305-321. Associated files
42. H.J. Broersma, N. Bruin, J.L. Hurink, L.E. Meester, S.S. op de Beek, J.H. Westhuis, Throughput of ADSL modems, in Proceedings of the 33rd European Study Group with Industry, Syllabus 46: 11-26, CWI, Amsterdam (1999).
43. Nils Bruin, Generalization of the ABC-conjecture, Master Thesis, Leiden University, 1995. (pdf version)

Student Theses

1. Xu, Zhe, Toric analysis of symmetric differentials on A_n singularities, M.Sc., Summer 2023.
2. Chen, Yixin, Two-torsion of the Brauer group of an elliptic surface, M.Sc., Summer 2022.
3. Filatov, Evgueni, Brauer-Severi varieties associated to twists of the Burkhardt quartic, M.Sc., Summer 2020.
4. Lewis, Daniel, An implementation of two-cover descent on plane quartic curves, M.Sc., Summer 2019.
5. Yadegarzadeh, Sepehr, On the density of parameterizations of generalized Fermat equations of signature (2,3,3) that produce locally primitive solutions, M.Sc., Summer 2019.
6. Kulkarni, Avinash, Aspects of the arithmetic of uniquely trigonal genus four curves: arithmetic invariant theory and class groups of cubic number fields, Ph.D., Fall 2018.
7. Brett Nasserden, Arithmetic aspects of the Burkhardt quartic threefold, M.Sc., Summer 2016.
8. Navid Alaei, Symmetric Differential Forms on the Barth Sextic Surface, M.Sc., Spring 2015.
9. Avinash Alexander Kulkarni, On Jacobians of dimension 2g that decompose into Jacobians of dimension g, M.Sc., Summer 2014.
10. Patrick Ryan McMahon, Solvability of ternary equations of signature (3,3,2), M.Sc., Summer 2014.
11. Steven Kieffer, Computability in principle and in practice in algebraic number theory: Hensel to Zassenhaus, M.Sc., Spring 2012.
12. Alexander Molnar, Fractional linear minimal models of rational functions, M.Sc., Fall 2011. errata
13. Kevin Doerksen, On the arithmetic of genus 2 curves with (4,4)-split Jacobians, Ph.D., Summer 2011.
14. Brett Hemenway, On recognizing congruent primes, M.Sc., Fall 2006.