Sophie Marques

Research interests

I am currently Senior Lecturer, at Stellenbosch University, after 2 years of Post doc at UCT and 4 years at the Courant Institute, NYU as Visiting assistant professor and Clinical assistant professor. I am interested in extending ramification theory to Algebraic geometry. This also includes understanding the properties of the ring of invariants. More precisely, when the properties of a ring such as Cohen-Macaulayness are transferred into the ring of invariant and how this link with ramification. Moreover, I want to understand low field degree extensions. I would like to investigate the existence of radical closure and radical descent for those. For instance, she would like to classify such extensions, describe precisely their ramification, obtain explicit genus formulae, obtain explicit integral basis, describe moduli spaces… I truly enjoy linear Algebra and I am interested on understanding Linear Algebra concepts in a non communitative setting. I would also like to acquiert a more intuitive understanding of Zariski topology. I also do research in non commutative algebra near fields and near vector spaces.

Wisaarkhu

I planted the seed of the Wisaarkhu project, in 2019. This was created together with a team of amazing people and the Rubbi Fund. The aim is to show that mathematics is a human endeavour, despite its inhumanly pristine appearance and to encourage people to find ways in which mathematics can empower them to reach their goals, as opposed to just seeing it as a subject for mathematicians. The magazine was launched in March 2020. It is not uncommon to see psychology, history, neurobiology and economics, to name a few, side by side each contributing to the discussions and the magazine around a chosen theme. Contributors range from students to teachers and academics. Each piece is extensively reviewed and presented with carefully curated complementary art, contributed by artists on the team. Various articles have been written about us. We were also finalist of the Falling Walls in the science engagement category in 2020.

Published research papers

• Tame actions of affine group schemes and tame stacks, C. R. Acad. Sci. Paris. Ser. I, 350 (3-4):125-128, https://doi.org/10.1016/j.crma.2012.01.020 (2012).

• Existence of slices on a tame context, European Journal of Mathematics 1(1):54-77, https://doi.org/10.1007/s40879-014-0022-4 (2015).

• 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).

• Holomorphic differentials of solvable Galois towers of curves over a perfect field (joint with Kenneth Ward), Mathematische Nachrichten, https://doi.org/10.1002/mana.201500347 (2018).

• Cubic fields: a primer (with Kenneth Ward), European Journal of Mathematics, https://doi.org/10.1007/s40879-018-0258-5 (2018).

• 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).

• When are permutation invariants Cohen-Macaulay over all fields? (with Ben Blum Smith), in Algebra and Number Theory, Vol. 12 , No. 7, 1787–1821 https://doi.org/10.2140/ant.2018.12.1787 (2018)

• 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).

• 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)

• 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)

• Toward an intuitive understanding of the structure of near-vector spaces. (with Karin-Therese Howell). Accepted for publication in Communication in Algebra. Available at https://arxiv.org/pdf/1912.06674.pdf (2020)

Books

• Linear Algebra I Frederick P. Greenleaf and Sophie Marques, ISBN-10: 1-4704-4871-8, ISBN-13: 978-1-4704-4871-4 (2019)

• Linear Algebra II Frederick P. Greenleaf and Sophie Marques, ISBN-10: 1-4704-5425-4, ISBN-13: 978-1-4704-5425-8 (2020)

Preprints

• Cubic fields: A primer (joint with Kenneth Ward). Full version, available at https://arxiv.org/pdf/1703.06219.pdf. (2017).

• A complete classification of cubic function fields over any field (joint with Kenneth Ward). Available at https://arxiv.org/pdf/1612.03534.pdf (2017).

• Tame action on affine group schemes and tame stacks, PhD Thesis. PDF (2013).

• Near-field structures induced by multiplicative automorphisms, their limits, and generalized means for complex numbers. (2022)