Kéva Djambaé

Research interests

I am currently a PhD student under the supervision of Gaëtan Bisson and David Kohel. I am a member of the GAATI Laboratory at the University of French Polynesia and of the Arithmetic and Information Theory (ATI) team within the Institute of Mathematics of Marseille (I2M) .
A curriculum vitae (September 2026) is available here.

I specialize in arithmetic geometry, a field at the intersection of algebraic number theory and algebraic geometry. My Master's thesis focused on the generalization of the Kronecker-Weber theorem in the setting of totally imaginary quadratic extensions, using elliptic curves with complex multiplication. The final version of the thesis and an English summary are available below:

• Master's thesis: Autour du douzième problème de Hilbert
• A summary of the Master's thesis

My research focuses on abelian varieties, with a particular interest in the explicit construction of field automorphisms from isogeny cycles. This work offers new perspectives on the arithmetic structure of finite and local fields by linking isogeny theory with field extensions and Galois actions.
I am interested in both computational and theoretical aspects, primarily using SageMath and Magma to produce explicit examples. My approach combines class field theory and scheme theory, allowing me to explore the interactions between arithmetic invariants, field extensions, and geometric objects within a framework that is both concrete and unified.

Published / Accepted Articles

• Automorphisms of finite fields from isogeny cycles (2027). Finite Fields and Their Applications, 2027, 118, pp.102922. <j.ffa.2026.102922>
  • A note written for the 2026 UPF Doctoriales: "Automorphisms of finite fields from isogeny cycles" <hal-05581754>
  • Magma code illustrating the article is available here .

Current Project

• Automorphisms of local fields from isogeny cycles (2026)

Popularization

• Poster for the 2025 UPF Doctoriales, titled "Elliptic Curves over Finite Fields". <hal-05575112>

Upcoming talks

No talks are currently scheduled (please feel free to contact me by email if you'd like to invite me to present my work.).

Past talks

I have given several talks in academic and outreach settings:

• A 30-minute presentation of my research at the Conseil économique, social et culturel de Polynésie française , on May 21, 2026.
• A 15-minute presentation at the 2026 UPF Doctoriales, entitled "Number Theory from a Geometric Perspective". This event resulted in a publication available here.
• A presentation at the Number Theory Seminar at the University of New South Wales in Sydney, Australia, on April 15, 2026, entitled "Explicit construction of Galois Group".
• An outreach talk at the SOUPAMES seminar , organized by the ANU-CNRS France Australia Mathematical Sciences and Interactions International Research Lab in Canberra from April 7 to 10, 2026, entitled "Number theory through the lens of geometry".
• A 15-minute presentation at the SOUPAMES seminar , organized by the ANU-CNRS France Australia Mathematical Sciences and Interactions International Research Lab in Canberra from April 7 to 10, 2026, entitled "Explicit construction of Galois Group".
• A team seminar at the GAATI Laboratory on January 26, 2026, entitled "Automorphisms of finite fields from an elliptic curve".
• A team seminar at the GAATI Laboratory on May 13, 2025, entitled "Galois Action and Elliptic Curves", where I presented my annual research work and my Master's thesis.
• A presentation at the 2025 UPF Doctoriales aimed at a general audience. A recording is available here (my presentation starts at 27:30), together with the poster.
• I organized a mathematical outreach workshop at l'École de la Deuxième Chance in Marseille , at the invitation of J. Youssef, on July 22, 2022.

2026/2027

In 2026/2027, I have the same teaching load as in 2025/2026: three tutorial groups (TD) for first-year students in the Mathematics - Engineering Sciences program at the University of French Polynesia (UPF).
Unless otherwise specified, the tutorial sheets are written by the professors

First semester

• Numerical and Algebraic Calculus
  • Lecture given by Christophe Raffalli
  • Tutorial 0 : Diagnostic Assessment (written by myself)
  • Tutorial 1 : Rational and real numbers; equations and inequalities; Notable Identities
  • Tutorial 1 bis : Additional exercises
  • Tutorial 2 : Complex Numbers

Second semester

• Matrix Calculus
  • Lecture given by Prescillia Tcheou
  • TD to be announced

2025/2026

In 2025/2026, I taught three tutorial groups (TD) for first-year students in the Mathematics - Engineering Sciences program at the University of French Polynesia (UPF).
Unless otherwise specified, the tutorial sheets were written by the professors responsible for the lectures:

First semester

• Numerical and Algebraic Calculus
  • Lecture given by Christophe Raffalli
  • TD 1: Rational and real numbers; equations and inequalities; remarkable identities
  • TD 2: Complex numbers
  • Two proofs for the complex roots of i (written by myself)
  • TD 3: Polynomials
  • TD 4: Rational functions
  • Additional exercises

Second semester

• Matrix Calculus
  • Lecture given by Prescillia Tcheou
  • TD
  • A summary sheet on determinants
  • TD n° 2 (written by myself)
  • Review sheet (written by myself)

2024/2025

In 2024/2025, I taught two tutorial groups during the second semester as part of the first-year Mathematics - Engineering Sciences program at the University of French Polynesia (UPF).
The tutorial sheets were written by the professors responsible for the lectures:

• Integral Calculus
  • Lecture course taught by Jean Vallès
  • Integral Calculus
  • Integration by parts and change of variables
  • Taylor expansions
  • Review sheet
  • Differential equations
  • Review sheet 2 (prepared by Christophe Raffalli and myself)
• Matrix Calculus
  • Lecture course taught by Prescillia Tcheou
  • TD

2023/2024

I began my teaching career at Lycée Honoré Daumier in Marseille, where I taught one Seconde class and two Première générale classes as part of the CAPES internship.
Some course notes are provided below, although they are incomplete due to time constraints. Please feel free to contact me by email if you notice any errors:

• Seconde générale 2023/2024
• Première générale 2023/2024

Research Commission

Elected member representing PhD students from the Sciences, Technologies and Health (STS) sector on the Research Commission of the University of French Polynesia (2025–2027 term), contributing to discussions on scientific orientations, research evaluation and support, as well as doctoral student representation.

Disciplinary Commission

Elected member of the users' section of the Disciplinary Commission of the University of French Polynesia (2025–2027 term), contributing to deliberations concerning compliance with academic obligations, the examination of disciplinary matters, and the safeguarding of students' rights.