I'm a fourth year PhD student supervised by Prof. Samir Siksek and Dr Damiano Testa. I'm due to graduate in the summer of 2024.

My main interests are in arithmetic geometry and computational number theory.

I'm interested methods to compute explicit torsion points on Jacobians of curves of small genus and applications of these. Some of my current projects involve the study of modular curves, their rational and integral points, modular units and torsion subgroups of modular Jacobians.

I'm one of the organisers of "Modular Curves and their Arithmetic": MCA

Papers and Preprints

3-Torsion Subgroups of Jacobians of Plane Quartics (January 2024, joint with J.Rawson)

Computing Cuspidal Subgroups of Modular Jacobians (August 2023)

Three-Torsion Subgroups and Conductors of Genus 3 Hyperelliptic Curves (October 2022)

Two-Torsion Subgroups of Some Modular Jacobians (May 2022, to appear in the International Journal of Number Theory)

Talks

Rational Cuspidal Points on the Modular Jacobians $J_{H}\left( p \right)$, Modular Curves and Galois Representations, Zagreb, September 2023

Cuspial Points on Modular Jacobians, Workshop on Arithmetic and Algebra of Rational Points, Bristol, September 2023

Rational Cuspidal Points on Modular Jacobians, Y-RANT, September 2023

Two-Torsion Subgroups of Jacobians of Non-Hyperelliptic Curves, Bayreuth, May 2023

Rational Points on Modular Jacobians, The Seventh Mini Symposium of the Roman Number Theory Association, May 2023

Rational Points on Modular Jacobians, WINGS, April 2023

Computing 3-torsion Points on Jacobians of Genus 3 Hyperelliptic Curves, Linfoot Seminar Bristol, March 2023

Two-Torsion Subgroups of Jacobians of Genus 5 Curves, Manchester Number Theory Seminar, November 2022

Two-Torsion Subgroups of Genus 5 Curves and the Generalised Ogg Conjecture, Warwick Junior Number Theory Seminar, October 2022

Two-Torsion Subgroups of Jacobians of Genus 5 Curves, Y-RANT Glasgow, August 2022

Miscellaneous

My MMath project on the class number of Z_p extensions : DiscriminantBoundsandClassNumber (supervised by Prof. Samir Siksek)

Email: e.lupoian@warwick.ac.uk