Francesca Bianchi
Email: francesca.bianchi.maths [at] gmail.com
Until January 2023 I was a Postdoc in the Algebra group at the University of Groningen.
I completed my DPhil in 2019 at the University of Oxford, under the supervision of Jennifer Balakrishnan and Alan Lauder.
Publications and preprints
Algorithms for p-adic Heights on Hyperelliptic Curves of Arbitrary Reduction (with E. Kaya, J. S. Müller).
Coleman-Gross Heights and p-adic Néron Functions on Jacobians of Genus 2 Curves (with E. Kaya, J. S. Müller).
p-Adic sigma functions and heights on Jacobians of genus 2 curves.
Rational points on rank 2 genus 2 bielliptic curves in the LMFDB, (with O. Padurariu), to appear in LuCaNT: LMFDB, Computation, and Number Theory, Contemporary Mathematics.
Q(sqrt(-3))-Integral Points on a Mordell Curve , Mathematical Software – ICMS 2020, Vol 12097, Springer (2020), 39-50 .
Two recent p-adic approaches towards the (effective) Mordell conjecture , (with J. S. Balakrishnan, A. J. Best, B. Lawrence, J. S. Müller, N. Triantafillou, J. Vonk), Arithmetic L-functions and differential geometric methods, Birkhäuser (2021), 31-74.
Explicit quadratic Chabauty over number fields (with J. S. Balakrishnan, A. Besser, J. S. Müller) , Israel Journal of Mathematics, Vol. 243, No. 1 (2021), 185–232.
Quadratic Chabauty for (bi)elliptic curves and Kim's conjecture, Algebra & Number Theory, Vol. 14, No. 9 (2020), 2369-2416.
Chabauty-Coleman experiments for genus 3 hyperelliptic curves , (with J. S. Balakrishnan, V. Cantoral-Farfán, M. Çiperiani, A. Etropolski), Research Directions in Number Theory, Association for Women in Mathematics Series, Vol. 19, Springer (2019), 67–90 .
Consequences of the functional equation of the p-adic L-function of an elliptic curve , Functiones et Approximatio, Commentarii Mathematici, Vol. 60, No. 2 (2019), 227-236.
The coronal energy input from magnetic braiding , (with A.R. Yeates, B. T. Welsh, P. J. Bushby) , Astronomy & Astrophysics Vol 564 : A131, (2014).