Find me on: arXiv, GitHub, ORCiD, Stack Exchange.

Research interests

• Data science and machine learning.
• Kernel density estimation.
• Computational p-adics.
• Galois theory and ramification theory.
• Factorization and root-finding of systems of equations.

Papers & Reports

• Exact p-adic computation in Magma, Journal of Symbolic Computation (accepted 2020). (Accepted PDF, arXiv, DOI)
• Data Study Group Network Final Report - Woolfson Laboratory, with several co-authors, Alan Turing Institute (June 2020). Workshop on predicting oligomeric protein structure from amino acid sequences. (report, DOI)
• Guiding Principles for Unlocking the Workforce - What Can Mathematics Tell Us?, with many authors, Knowledge Transfer Network, Isaac Newton Institute & International Centre for Mathematical Sciences (working paper, 2020). Workshop on mathematical principles for easing the COVID-19 lockdown. (homepage, PDF)
• Computing the Galois group of a p-adic polynomial, Int. J. Number Theory (2020). (overview, tables, arXiv, DOI)
• 3-torsion and conductor of genus 2 curves, with T. Dokchitser, Math. Comput. (2018). (overview, article, arXiv)
• PhD Thesis: Aspects of p-adic computation, Bristol University (2019). (thesis)
• ExactpAdics: An exact representation of p-adic numbers, pre-print (2018). (overview, arXiv)
• On enumerating extensions of p-adic fields with given invariants, pre-print (2018). (overview, arXiv)

Tables

• Galois groups of p-adic fields.

Code

• PythonCall.jl: Call Python code from Julia and vice-versa.
• Bokeh.jl: Julia bindings for the BokehJS plotting library.
• ARFFFiles.jl: For loading and saving ARFF (Attribute Relation File Format) files.
• Countries.jl: For handling the countries on Earth.
• CustomAxes.jl: Arrays supporting customized axes, such as names and labels.
• ShadeYourData.jl: Interactive plotting of millions of data points.
• Edlib.jl: Julia bindings for the edlib string alignment library.
• MagmaCall.jl: Call Magma code from Julia.
• LTWA.jl: Produce abbreviations using ISO 4 and the List of Word Title Abbreviations.
• LogarithmicNumbers.jl: Implementation of a logarithmic number system for Julia.
• Infinity.jl: Julia package to extend the integers, or any other real type, with infinity.
• ExactpAdics2 (github): User-friendly package for performing p-adic computations exactly. Newer implementation, recommended. (See the article “ExactpAdics…”.)
• ExactpAdics (github): User-friendly package for performing p-adic computations exactly. First implementation, generally slower than ExactpAdics2. (See the article “ExactpAdics…”.)
• Genus2Conductor (github): For computing the conductor of a genus 2 hyperelliptic curve. (See the article “3-torsion…”.)
• pAdicGaloisGroup (github): Experimental code for computing Galois groups over p-adic fields.
• pAdicExtensions (github): For computing extensions of p-adic fields. (See the article “On enumerating extensions…”.)
• MagmaUtils (github): Adds extra basic functionality to Magma.
• magdoc (github): For automatically generating documentation from Magma code.
• sublime-magma (github): Magma language support for the Sublime text editor.
• sublime-magma-snippets (github): Magma snippets for Sublime.

Articles

• Given n red and n blue points, the total monochromatic distance is less than the total bichromatic distance. (MathSE)
• On computing the Galois group of a rational polynomial. (MathSE)
• When we adjoin one root of a polynomial to a field, how many other roots do we get? (MathSE)
• Counting p-adic fields with certain properties. (MathOverflow)
• Why a normal extension of a normal extension of a field is not normal. (MathSE)
• Trace and discriminant of a field extension are independent. (MathOverflow)
• Why algebraic numbers are a field. (MathSE)
• Minimal polynomial of ab when those of a and b are known. (MathSE)

Resume

• 2020-: Senior data scientist, Alan Turing Institiute.
• 2018-2020: Heilbronn research fellow, University of Bristol.
• 2014-2018: PhD mathematics, University of Bristol. Supervisor: Tim Dokchitser.
• 2008-2009: Part III/MMath (Distinction), University of Cambridge.
• 2005-2008: BSc mathematics (Class I), University of Cambridge.