Exploring polynomial equations through Field Theory

In this talk, we explore the intricate connections between polynomial equations, field theory, and the fascinating realm of roots of unity. Drawing on recent research advancements, we will present compelling examples that illustrate the significance of our collaborative work with Kenneth Ward, Mpendulo Cele, Elizabeth Mrema, Chad Brache Valentijn Karemaker, and Jeroen Sijsling. Together, we have explored intriguing concepts such as radical closure, Artin-Schreier closure, and elementary closure, with a particular focus on the roots of unity.

Through our discussions, we will shed light on the profound connections between polynomials, field theory, and roots of unity, revealing their intrinsic relationship and their impact on modern mathematical research. By the end of the talk, participants will gain new insights into the rich tapestry of these concepts and discover exciting research directions that lie ahead.


  1. Generic polynomials for cyclic function field extensions over certain finite fields. European Journal of Mathematics, 4(2):585-602, https://doi.org/10.1007/s40879-017-0188-7 (2017).
  2. Cubic fields: a primer (with Kenneth Ward), European Journal of Mathematics, https://doi.org/10.1007/s40879-018-0258-5 (2018).
  3. An explicit triangular integral basis for any separable cubic extension of a function field (with Kenneth Ward), European Journal of Mathematics, https://doi.org/10.1007/ s40879-018-0243-z., (2018).
  4. A complete study of the ramification for any separable cubic global function field, (with Kenneth Ward) Research in Number Theory 5, 36, https://link.springer.com/article/10.1007/s40993-019-0173-y (2019).
  5. The Geometry Of The Moduli Space Of non-cyclic Biquadratic Field Extensions. (with Mpendulo Cele).  Quaestiones Mathematica,  https://doi.org/10.2989/16073606.2021.1951391 (2021).
  6. Cubic function fields with prescribed ramification. (with Valentijn Karemaker and Jeroen Sijsling). International Journal of Number Theory. Vol. 17, No. 09, pp. 2019-2053, https://doi.org/10.1142/S1793042121500755 (2021).
  7. Quadratic cyclotomic moduli spaces. (with Elizabeth Mrema). https://arxiv.org/abs/2210.03563 2022.
Date:  2023-09-05
Start Time:   15:00
Speaker:  Sophie Marques (Stellenbosch Univ., South Africa)
Institution:  Stellenbosch University
Place:  Sala 5.5, DMUC
Research Groups: -Algebra, Logic and Topology
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