Hi, I'm Sophie
PhD student | pi calculator Graduated summer 2024 with a 1st class MMath from the University of Edinburgh. Now pursuing a PhD at the University of Edinburgh under Prof. Antony Maciocia, focusing on algebraic geometry and category theory. 
Pi Day
I've been involved in two epic sessions of calculating pi by hand, working with Matt Parker in 2022 and 2024. Check the videos out here: My Papers So far on my mathematical journey I've had the pleasure of working with some brilliant mathematicians, exploring exciting areas of mathematics. Feel free to dive into the papers below and sate your mathematical hunger!
Positivity and Integrality of Mirror Maps
May 2024
This paper explores the application of mirror maps to reflexive polytopes in Algebraic Geometry. In my dissertation I found that these mirror map power series have all integer coefficients, and that a variant map produces series with all positive integers. The preprint is available here. Read Full Paper 
Discrete Morse theory
Summer 2023
This paper, developed during a 2023 summer project with Dr. Jeff Hicks, presents a combinatorial proof that the square of the differential is zero in simplicial complexes. Key concepts include differential definition and sign assignment within a simplicial complex. The findings were shared at the IMA TMT conference, and the presentation is available here. Read Full Paper
Brace theory
Winter 2022
This project was the final assessment for a reading course on the representation theory of the symmetric group, focusing on Coxeter groups in vector spaces. Read Full Paper
Coxeter groups
Winter 2023
This project was the final assessment for a reading course on the representation theory of the symmetric group, focusing on Coxeter groups in vector spaces. The course, supervised by Dr. Pavel Safronov, was one of two he oversaw during my undergraduate studies, and I highly recommend his courses or reading groups if given the opportunity. Read Full Paper
Covering spaces of the figure of eight
Summer 2021
During the summer of 2021, I explored Algebraic Topology, focusing on the covering spaces of the figure-eight in an unpaid project under Prof. Jon Pridham. I incorporated my interest in Celtic knots into the research and shared my findings in Chalkdust magazine, available here. Read Full Paper