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Mathematics Institute

Diana Mocanu

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:
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:
  • VIVA Presentation (slidesLink opens in a new window), Warwick 2024.
  • "Variants of the Modular Method", Yrant 2024, Oxford (slidesLink opens in a new window).
  • "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 an rth power plus an rth power is a pth power over totally real number fields", Yrant 2023 (slidesLink opens in a new window)
  • "The modular approach for solving an rth power plus an rth power is a pth power over totally real number fields" (online), 14th Ukraine Algebra Conference (link), Sumy, Ukraine, July 2023.
  • "The modular approach for solving an rth power plus an rth power is a pth power 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 an rth power plus an rth power is a pth power 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:
Contact:

Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL

Office: B3.04

diana dot mocanu at warwick dot ac dot uk