Sophie Marques

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20242026

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math.AC2025

Comparing the face rings of a boolean complex and its barycentric subdivision

Ben Blum-Smith, Sophie Marques

We consider the relationship between the Stanley--Reisner ring (a.k.a. face ring) of a simplicial or boolean complex $Δ$ and that of its barycentric subdivision. These rings share…

math.AG2025

A note on gluing: a pillar of algebraic geometry

Sophie Marques, Damas Mgani

This paper examines the concept of gluing, placing it within its most general categorical context and tracing its foundational role in the broader architecture of algebraic geometr…

math.CO2025

A study of a recursive sequence of polynomials revealing weighted Catalan Numbers

Sophie Marques, Elizabeth Mrema

This paper examines the recursive sequence of polynomials $p_{n} (x)$ , defined by $p_{0} (x) = x^{2} - 2$ and $p_{n} (x) = p_{n - 1} (x)^{2} - 2$ for $n \geq 1$ . It describes the field-theoretic m…