George Țurcaș
Lecturer in the Geometry group at Babeș-Bolyai University. My research lies in Number Theory: Diophantine applications of modularity, Galois representations and Bianchi modular forms.
About
I am a lecturer in the Geometry group at Babeș-Bolyai University. Previously I held postdoctoral positions at IMAR and the University of Warwick. I obtained my PhD from the University of Warwick under the supervision of Professor Samir Siksek. Before that I was an MASt (Part III) student at the University of Cambridge.
My research interests include Diophantine applications of modularity, Galois representations and Bianchi modular forms.
Research Overview
My work explores aspects of modern Number Theory at the interface of Diophantine geometry, the theory of elliptic curves and modular (including Bianchi modular) forms. A recurring theme is leveraging modularity and properties of Galois representations to resolve arithmetic problems over number fields.
- Elliptic curves & isogenies
- Galois representations
- Modularity & Serre-type conjectures
- Bianchi modular forms
- Diophantine equations
Selected Publications & Writings
For full list of publications please see my Google Scholar profile.
- (with Barcau and Pașol) Composing bridges, Information and Computation, 2025. doi
- 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)
- (with Andrica) Pairs of Rational Triangles with Equal Symmetric Invariants, Journal of Number Theory, 2021. doi preprint
- (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
- On Serre’s modularity conjecture and Fermat’s equation over quadratic imaginary fields of class number one, Journal of Number Theory, 2019. doi arXiv
- Diophantine applications of Serre’s modularity conjecture, PhD thesis, University of Warwick, 2019. pdf
- Irreducible binary cubics and the Generalized Superelliptic Equation over number fields, Acta Arithmetica. doi arXiv
- On Fermat’s equation over some quadratic imaginary number fields, Research in Number Theory, 2018. journal
- On the BSD Conjecture, Expository essay (Part III, Cambridge). pdf
Teaching
Recent & current courses (selection):
- Affine Geometry (Year 1, Maths & CS, English)
- Complements of Geometry (Year 2, Maths & CS, English)
- Geometrie afină (Matematică-Informatică, anul I)
- Teme de geometrie I (Masterat Didactic)
All course communications via dedicated MS Teams groups. Office hours: Thursdays 12–14 (appointment by email, ≥24h notice).
Lecture Notes & Resources
Here are some Algebraic Number Theory notes I typed while attending a course given by Dr. Jack Thorne (Part III, Cambridge): ANT – Part III Cambridge (PDF).
Weekly Schedule (Semester 2024–2)
Monday
- No scheduled teaching
Tuesday
- 09:00–17:00 Student meetings (Bachelor theses / dissertations) & office hours (upon request)
Wednesday
- 12:00–14:00 Geometrie 2 (Geometrie afină) Seminar (Room A313)
- 14:00–16:00 Geometrie 2 (Geometrie afină) Seminar (Room A322)
Thursday
- 08:00–10:00 Complemente de geometrie (Lecture) Room 7/I (MIE2)
- 10:00–12:00 Complemente de geometrie (Seminar) Room 7/I (MIE2)
Friday
- 12:00–14:00 Colectiv: Geometrie (Group activities)
- 14:00–16:00 Teme de geometrie I (Course) Room e
- 16:00–17:00 Teme de geometrie I (Seminar) Room e
According to the official timetable: Orar 2024–2. Tuesday meetings by prior email arrangement.
Selected Talks & Events
- 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
Contact
Email: george dot turcas at ubbcluj.ro
Postal Address:
Colectivul de Geometrie, UBB
Mathematica
Strada Ploiești 27
Cluj-Napoca 400000
Romania