I am a fourth-year PhD student under the supervision of Prof. Samir Siksek. I am currently working on the study of Diophantine equations over totally real fields, using the modularity of certain elliptic curves and the study of S-unit equations. However, my interests include more vast aspects of algebraic number theory, arithmetic geometry, and more recently isogeny-based cryptography.

I previously finished my MMath degree at the University of Oxford. My dissertation was on "Profinite Groups as Galois Groups" under the supervision of Prof. Nikolay NikolovLink opens in a new window.

Writings:

• "Asymptotic Fermat for signatures (r, r, p) using the modular approach", Research in Number Theory, Volume 9, Issue 4, Article Number 71, (linkLink opens in a new window)(arXivLink opens in a new window);
• "Asymptotic Fermat for signatures (p,p,2) and (p,p,3) over totally real fields", Mathematika, Volume 68, Issue 4, Pages 1233-1257 (linkLink opens in a new window)(arXivLink opens in a new window), based on the first-year summer project under the supervision of Samir Siksek;
• "Mary Somerville's Diophantine Equations" (PDFLink opens in a new window ), under the supervision of Minhyong Kim;
• "Elliptic Curves in Cryptography" (PDFLink opens in a new window ), handout as part of MBL 2021Link opens in a new window (not attended in person due to unexpected circumstances).

Teaching and Other Responsibilities:

• Teaching assistant for the third-year module Galois Theory, Term 1, 2023;
• Teaching assistant for Modularity and Diophantine Equation course as part of the Introduction to SAGA school, CIRM, Marseille, 2022;
• Supervisor for first-year Mathematics undergraduates, for the modules Analysis I, Algebra I, and Mathematical Modelling, Term 1 & 2, 2022-2023;
• Teaching assistant for the second-year module Geometry, Term 1, 2022;
• Exam marking (resits) for the second-year module Linear Algebra, Summer 2022;
• Teaching assistant for the fourth-year module Reflection Groups, Term 2, 2022, 2023;
• Teaching assistant (online) for the third-year module Groups & Representations, Term 1, 2021;
• Exam marking for the third-year module Algebraic Number Theory, Term 3, 2021;
• Supervisor (online) for first-year Mathematics and Statistics undergraduates for the modules Mathematical Analysis I and II, Linear Algebra, Terms 1 and 2, 2020-2021.

Conferences and Summer Schools Attended:

• Workshop on Arithmetic and Algebra of Rational Points, Bristol, UK, September 2023;
• 14th Ukraine Algebra Conference (online), Sumy, Ukraine, July 2023;
• Representation Theory XVIII Conference, Number Theory section, Dubrovnik, Croatia, June 2023;
• An Expedition into Arithmetic Geometry, Lorentz Center, Leiden, The Netherlands, May-June 2023;
• WINGs (Women in Number Theory and Geometry), Chesterfield, UK, April 2023 (organizer);
• Introduction to SAGA (school and conference), CIRM, Marseille, France, January - February 2023;
• Mordell 2022, Cambridge, UK, August 2022;
• Elliptic Curves Graduate School, Baskerville Hall, UK, August 2022;
• ICM Sectional Number Theory and Geometry, Zurich, Switzerland, July 2022;
• Modern Breakthroughs in Diophantine Problems, Banff, Canada, June 2022;
• Women in Number Theory and Geometry (WINGS), West Lexham, UK, June 2022;
• Isogeny-based Cryptography School (online), July-September 2021;
• Arithmetic, Geometry, Cryptography and Coding Theory, CIRM (online), May-June 2021;
• WIMP (Warwick-Imperial) Autumn 2020 Conference (online), 28-29th November 2020.

Talks given:

• "Conductor computations for the modular method via cluster pictures", Modular Curves and their Arithmetic, University of Warwick 2023 (slidesLink opens in a new window).
• "The modular approach for solving over totally real number fields", Yrant 2023 (slidesLink opens in a new window)
• "The modular approach for solving over totally real number fields" (online), 14th Ukraine Algebra Conference (link), Sumy, Ukraine, July 2023.
• "The modular approach for solving over totally real number fields", Representation Theory XVIII Conference, Number Theory section, Dubrovnik, Croatia, June 2023;
• "Mary Somerville's Diophantine equations", Postgraduate Seminar, Warwick (slidesLink opens in a new window);

• "The modular approach for solving over totally real number fields", Institute de Mathématiques de Marseille, November 2022 (slidesLink opens in a new window);

• "The Modular Approach to Diophantine Equations over totally real fields", Linfoot Number theory seminar University of Bristol, October 2022;
• "The Modular Approach to Diophantine Equations over totally real fields", BIRS 2022Link opens in a new window.
• "The Modular Approach to Diophantine Equations over totally real fields for signatures (p,p,2) and (p,p,3)" (online), CTNT 2022Link opens in a new window;
• "The Modular Approach to Diophantine Equations over totally real fields", WINGS 2022Link opens in a new window;
• "Group Schemes", Mazur's Torsion Theorem Reading Group (linkLink opens in a new window), 4th April 2022;
• "Prime Ideal Theorem", Random Polynomials Reading Group, University of Warwick, 25th February 2022;
• "Elliptic Curves in Cryptography" (slidesLink opens in a new window), Postgraduate Seminar, University of Warwick, 26th January 2022;
• "Elliptic curves over the complex numbers and lattices", Modular Forms Reading Group (online), University of Warwick, 5th February 2021;
• "Borel Subgroups", Algebraic Groups Reading Group (online), University of Warwick, 25th November 2020;
• "Galois Cohomology", Class Field Theory Reading Group (online), University of Warwick, 30th October 2020.

(Co-)Organizer:

• WINGs 2023, Chesterfield (linkLink opens in a new window);
• "Isogeny-based Cryptography" Study Group for the Warwick Number Theory Group, Term 1, 2022.
• President of the Invariants (Oxford University Mathematics Society), 2018-2019 (link).

Contact:

Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL

Office: B3.04

diana dot mocanu at warwick dot ac dot uk