# Research

## Publications

Files linked as direct .pdf files are typically the most updated versions with the fewest typos. This is sometimes ahead of the arXiv file, though the numbering and content will be identical in the limit.

- Attainable forms of Assouad spectra
Journal: *Preprint*(submitted)Links: pdfarxiv - Attainable forms of intermediate dimensions
With: Amlan Banaji Journal: *Ann. Fenn. Math.***47**(2022), 939-960Links: pdfdoiarxiv - A Multifractal Decomposition for Self-similar Measures with Exact Overlaps
Journal: *Preprint*(submitted)Links: pdfarxiv - Local Dimensions of Self-similar Measures Satisfying the Finite Neighbour Condition
With: Kathryn E. Hare Journal: *Nonlinearity*(to appear)Links: pdfarxiv - Geometric and Combinatorial Properties of Self-similar Multifractal Measures
Journal: *Ergod. Theory Dyn. Syst.*(to appear)Links: pdfdoiarxiv - When the Weak Separation Condition implies the Generalized Finite Type Condition
With: Kathryn E. Hare, Kevin G. Hare Journal: *Proc. Amer. Math. Soc.***149**(2021), 1555-1568Links: pdfdoiarxiv

## Software

Description | Language | Links |
---|---|---|

An automatic LaTeX project templater | Python | pypigithub |

Manage (Neo)Vim sessions | Fish | github |

Query adjacency properties of four-letter words | C | github |

## Presentations

- Jul. 2022 - Attainable forms of intermediate dimensions - BECMC 2022 (slides)
- Jul. 2022 - Dimension theory and classification of Assouad spectra through homogeneous Moran sets - University of Vienna Ergodic Theory Seminar
- Jun. 2022 - Classifying Dimension Spectra - Geometry of Deterministic and Random Fractals (slides)
- May. 2022 - Geometric and Combinatorial Properties of Self-similar Measures - Workshop on Self-affine and Overlapping IFS (poster)
- Apr. 2022 - Pisot Numbers and Bernoulli Convolutions - St Andrews Burn Meet (slides)
- Apr. 2022 - Geometric and Combinatorial Properties of Self-similar Measures - Probability, Analysis, and Dynamics 2022 (poster)
- Feb. 2022 - Attainable forms of intermediate dimensions - St Andrews Analysis Seminar
- Apr. 2021 - Self-similar measures with non-concave spectra and multifractal analysis - Junior Ergodic Theory Seminar (slides)
- Jan. 2021 - Analysis Group Intro Talk - St Andrews Online Burn Meet (slides)
- Oct. 2020 - Multifractal Analysis for Self-Similar Measures with Exact Overlaps - St Andrews Analysis Seminar (slidesvideo)
- Feb. 2020 - Geometric and Combinatorial Separation Conditions for IFSs - University of Waterloo Analysis Seminar (slides)
- Jul. 2019 - An Algebraic Proof of Quadratic Reciprocity - CUMC 2019
- Jul. 2018 - Pisot-Vijayaraghavan numbers - CUMC 2018