Publications

Published or accepted papers:

1. An algorithm to solve any tropical linear system Ax=Bx (joint work with M.J. de la Puente), Linear Algebra and its Applications, 435(4) (2011) 884–901.

2. Bad reduction of genus 3 curves with complex multiplication (joint work with I. Bouw, J. Cooley, K. Lauter, M. Manes, R. Newton, E. Ozman), Women in Numbers Europe, research Directions in Number Theory, Springer (2015), 109–151.

3. Twists of non-hyperelliptic curves, Revista Matemática Iberoamericana, 33 (2017), no. 1, 169–182.

4. Statistics for biquadratic covers of the projective line over finite fields with an appendix by A. Bucur (joint work with G. Meleleo, P. Milione), Journal of Number Theory, 173 (2017), 448–477.

5. Isogenies for Point Counting on Genus two Hyperelliptic Curves with Maximal RM (joint work with S. Ballentine, A. Guillevic, C. Martindale, M. Massierer, B. Smith, J. Top), Algebraic Geometry for Coding Theory and Cryptography, Assoc. Women math. Ser. 9, Springer (2017), 63–94.

6. On twists of smooth plane curves (joint work with E. Badr, F. Bars), Mathematics of Computation, Vol. 88, N. 315, January (2019),  pp 421–438.

7. Twists of genus 3 non-hyperelliptic curves, International Journal of Number Theory, Vol. 14, No. 6, (2018), 1785–1812.

8. Computing twists of hyperelliptic curves (joint work with D. Lombardo), Journal of Algebra, Volume 519, 1 February 2019,  pp 474–490.

9. Sato-Tate distributions of twists of the Fermat and the Klein quartics (joint work with F. Fité, A. Sutherland), Research in the Mathematical Science, 5:41 (2018), 40pp.

10. The Picard group of Brauer-Severi varieties (joint work with E. Badr, F. Bars), Open Mathematics, (2018), 16, 1196 – 1203.

11. Modular invariants for genus 3 hyperelliptic curves (joint work with S. Ionica, P. Kılıçer, K. Lauter, A. Manzateanu, M. Massierer, C. Vincent),  Research in Number Theory, (2019) 5: 9. https://doi.org/10.1007/s40993-018-0146-6 .

12. Primes dividing invariants of CM Picard curves (joint work with P. Kılıçer, M. Streng), Canadian Journal of Mathematics, (2020), Vol. 72, Issue 2, 480-504.

13. A note on the stratification by automorphisms of smooth plane curves of genus 6 (joints work with E. Badr), Colloquium Mathematicum, (2020), Vol. 159, No. 2, 207-222.

14. A bound on the primes of bad reduction of CM curves of genus 3 (joint work with P. Kılıçer, K. Lauter, R. Newton, E. Ozman, M. Streng), Proceedings of the  American Mathematical Society, 148, (2020), no. 7, 2843-2861.

15. Stable model of plane quartics with hyperelliptic reduction (joint work with R. Lercier, C. Ritzenthaler), to appear in Arithmetic, Geometry, Cryptography and Coding Theory, AMS Contemporary Mathematics, Vol. 770, (2021).

16. Reduction type of smooth plane quartics (joint work with R. Lercier, Q. Liu, C. Ritzenthaler), Algebra & Number Theory, 15-6 (2021), 1429-1468. DOI 10.2140/ant.2021.15.1429.

17. Reduction types of genus-3 curves in a special stratum of their moduli space (joint work with I. Bouw, N. Coppola, P. Kılıçer, S. Kunzweiler, A. Somoza), Assoc. Women Math. Ser., 24, Springer, Cham, 2021, 115–162.

18. Decomposing Jacobians via Galois covers (joint work with D. Lombardo, C. Ritzenthaler and J. Sijling), Experimental Mathematics, 32 (2023), no. 1, 218–240..

19. On different expressions for invariants of hyperelliptic curves of genus 3, Journal of the Mathematical Society of Japan, Vol. 74, No. 2 (2022).

20. Construction of Brauer-Severi varieties, Contemporary Mathematics, Volume 2 Issue 4, (2021). 

21. Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric (joint work with E. Camps Moreno, E. Gorla, C. Landolina, U. Martínez-Penas and F. Salizzoni), IEEE Transactions on Information Theory, Vol. 68, Issue 6 (2022), 3806-3822.

22. On smooth plane models for modular curves of Shimura type (joint work with S. Anni, E. Assaf), ANTS-XV proceedings, Research in Number Theory, (2023), no. 2, Paper No. 21, 20 pp.

23. Lower bound on the maximal number of rational points on curves over finite fields (joint work with J. Bergström, E. Howe, C. Ritzenthaler), Mathematical Proceedings of the Cambridge Philosophical Society, 176 (2024), no. 1, 213–238. 

24. Twists of the Klein quartic and counterexamples to the Hasse principle (joint work with M. Vullers), Indagationes Mathematicae, to appear.

25. Determining the primes of bad reduction CM curves of genus 3 (joint work with S. Ionica, P. Kılıçer, K. Lauter, A. Manzateanu, C. Vincent), The Quarterly Journal of Mathematics 75 (2024), no. 1, 239-276.

26. Refinaments of Katz-Sarnak theory for the number of points of curves over finite fields (joint work with J. Bergström, E. Howe, C. Ritzenthaler), Canadian Journal of Mathematics, to appear.

27. On invariants of Artin-Scheier curves (joint work with J. Duque-Rosero, H. Goodson, B. Malmskog, R. Scheidler), Assoc. Women Math. Ser., Springer, to appear.

28. Reduction of Plane Quartics and Dixmier-Ohno Invariants (joint work with R. van Bommel, J. Docking,  R. Lercier), ANTS-XVI proceedings, Research in Number Theory, to appear.

Preprints (available upon request) or submitted papers:

1. Sato-Tate distributions of Fermat hypersurfaces, Chapter 5 in my thesis.

2. Integer sequences that are generalized weights of a linear code (joint work with E. Gorla, U. Martínez-Peñas, F. Salizzoni), submitted.

3. Reduction of Plane Quartics and Cayley Octads (joint work with R. van Bommel, J. Docking, V. Dokchitser, R. Lercier), submitted.

4. On the conductor of Ciani plane quartics (joint work with I. Bouw, N. Coppola, A. Somoza), submitted.

5. Explicit height estimates for CM curves of genus 2 (joint work with L. Frey, S. Le Fourn), submitted.

Ph.D. thesis:

• Arithmetic Properties of non-hyperelliptic genus 3 curves (completed under the supervision of J.-C. Lario at Universitat Politècnica de Catalunya).

HDR thesis:

• Arithmetic Properties of genus 3 curves II (13-01-21, Université de Rennes 1).

Popularization notes:

• On the Sato-Tate Conjecture.