George Țurcaș

Selected Publications & Writings

For full list of publications please see my Google Scholar profile.

1. (with Diana Mocanu) New Algebraic Points on Covers of Elliptic Curves, 2026. preprint
2. (with Barcau and Pașol) Transversal Difference Numbers in Finite Abelian Quotients, 2026. preprint
3. (with Barbulescu, Barcau, and Pașol) Logarithmic Density of Rank ≥ 1 and Rank ≥ 2 Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography, accepted at ANTS XVII, to appear in Research in Number Theory, 2026. arXiv ANTS paper code
4. (with Gugulea, Lupașcu, Togan, and Turcaș) Privacy-Preserving Multi-Center Clinical Analytics with Threshold Homomorphic Encryption: A Pediatric Craniospinal Irradiation Use Case, Network Modeling Analysis in Health Informatics and Bioinformatics, 2026. preprint doi SharedIt (free access to published version)
5. (with Pop) Support-sensitive bounds for shortest zero-sum subsequences, 2025. preprint
6. (with Barcau and Pașol) Composing bridges, Information and Computation, 2025. doi
7. On the p-isogenies of elliptic curves with multiplicative reduction over quadratic fields, New Frontiers in Number Theory and Applications, Trends in Mathematics, Birkhäuser, 2024. doi preprint (pdf)
8. (with Barcau, Lupașcu and Pașol) Bridges Connecting Encryption Schemes, in Innovative Security Solutions for Information Technology and Communications (SecITC 2022), Lecture Notes in Computer Science, vol 13809, Springer, Cham, 2023. doi preprint (pdf)
9. (with Andrica) Pairs of Rational Triangles with Equal Symmetric Invariants, Journal of Number Theory, 2021. doi preprint
10. (with Najman) Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields, International Journal of Number Theory, 2021. doi arXiv
11. On Serre’s modularity conjecture and Fermat’s equation over quadratic imaginary fields of class number one, Journal of Number Theory, 2019. doi arXiv
12. Diophantine applications of Serre’s modularity conjecture, PhD thesis, University of Warwick, 2019. pdf
13. Irreducible binary cubics and the Generalized Superelliptic Equation over number fields, Acta Arithmetica. doi arXiv
14. On Fermat’s equation over some quadratic imaginary number fields, Research in Number Theory, 2018. journal
15. On the BSD Conjecture, Expository essay (Part III, Cambridge). pdf

Selected Talks & Events

• 07/2026 – ANTS XVII, Groningen (attending; tentative slides)
• 06/2026 – Bucharest-Shenzhen International Mathematics Conference, IMAR, Bucharest (invited talk; slides)
• 09/2023 – Modular Curves and Galois Representations, Zagreb (talk)
• 06/2023 – Tenth Congress of Romanian Mathematicians, Pitești (invited)
• 05/2023 – Workshop for Young Researchers in Mathematics, Iași
• 04/2023 – Algebra Seminar, University of Calabria
• 08/2022 – 10th Bucharest Number Theory Days, IMAR, Bucharest
• 03/2021 – Groningen Algebra Seminar (invited)
• 12/2020 – 8th Bucharest Number Theory Day (online)
• 12/2019 – Barcelona Fall Workshop on Number Theory II
• 09/2019 – Number Theory seminar, ICMAT, Madrid
• 08/2019 – 7th Bucharest Number Theory Day, Bucharest
• 06/2019 – Ninth Congress of Romanian Mathematicians, Galați
• 10/2018 – Young researchers in algebraic number theory, Sheffield
• 07/2018 – Building Bridges: EU/US Workshop on Automorphic Forms, Budapest
• 06/2018 – Torsion groups & Galois representations of elliptic curves, Zagreb
• 03/2018 – Linfoot seminar, Bristol
• 06/2017 – Journées Algophantiennes Bordelaises 2017, Bordeaux
• 05/2017 – Modular Forms are everywhere, Bonn
• 02/2017 – p-adic methods for Galois representations & modular forms, Barcelona
• 09/2016 – CMI Workshop: Recent Developments on Elliptic Curves, Oxford
• 09/2016 – Automorphic Forms: theory & computation, London
• 04/2016 – Explicit Methods in Number Theory (Cremona 60th), Warwick
• 03/2016 – British Mathematical Colloquium 2016, Bristol
• 03/2015 – Elliptic Curves, Modular Forms and Iwasawa Theory, Cambridge