Photo of me

Kenneth Moore's Homepage

I am a PhD student at the University of British Columbia. My master's degree is from the University of Alberta.

Publications and preprints

Publication 5

Avoiding short progressions in Euclidean Ramsey theory (2024+, submitted) — with Gabriel Currier and Chi Hoi Yip

We provide a general framework to construct colorings avoiding short monochromatic arithmetic progressions in Euclidean Ramsey theory.

Arxiv Preprint. Our resources page is here.

Publication 4

Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions (2024+, submitted) — with Gabriel Currier and Chi Hoi Yip

A conjecture of Erdos et. al. states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monochromatic congruent copy of every three-point configuration. This conjecture is known in some special cases. In this manuscript, we confirm one of the most natural open cases (stated in the title).

Arxiv Preprint. Our resources page is here.

Publication 3

On Axial Symmetry in Convex Bodies (2024+, submitted) — with Ritesh Goenka, Rui Sun, and Ethan White

We prove new upper and lower bounds on the minimal axiality (reflective symmetry) of planar convex sets, as well as the minimal folding symmetry. We also obtain the first (to our knowledge) exact upper bounds on hyperplane symmetry in any dimension.

Arxiv Preprint.

Publication 2

Improved estimates on the number of unit perimeter triangles (2023) — with Ritesh Goenka and Ethan White

We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.

Published in Discrete & Computational Geometry, or see the original Arxiv Preprint.

Publication 1

Bakry-Émery Ricci Curvature Bounds on Manifolds with Boundary (2023) — with Eric Woolgar

We prove a Bakry-Émery generalization of a theorem of Petersen and Wilhelm, that closed minimal hypersurfaces in a complete manifold with a suitable curvature bound must intersect. We then prove splitting theorems of Croke-Kleiner type for manifolds bounded by hypersurfaces obeying Bakry-Émery curvature bounds.

Published in the Journal of Mathematical Physics, or see the original Arxiv Preprint.

Publication 0

One Hundred and Twelve Point Three Degree Theorem (2020) — with Jacob Garber, Boyan Marinov, and George Tokarsky

We give a rigorous computer-assisted proof that a triangle has a periodic billiard path when all its angles are at most 112.3 degrees. This nears the apparent boundary for computerized methods occuring at 112.5 degrees.

Reviewed Version, or see the original Arxiv Preprint. Featured in Quanta Magazine.

Programming Projects

Project 1

Point sets with many unit distances

This page contains a list of point sets that form many unit distance pairs. To my knowledge, these are the best lower bounds for most small numbers.

Project page

Project 2

A program for finding low symmetry convex sets

One can use this program to easily check the axial symmetry of convex polygons, as well as run our searching algorithm to try to lower the current bound.

Project page

Project 3

Implementation of a circle packing algorithm

A surprising way of approximating conformal maps is with corresponding circle packings. This program implements an algorithm for finding such packings.

Project page

Project 4

Viewer for periodic path unfoldings

Periodic path unfoldings are very cumbersom to draw, so this program was designed to help make figures. The best takeaway from this project is the display of the amazing stable behaviour of certain periodic paths.

Project page

Project 5

Graph/digraph diagram maker

I wanted to quickly make a couple diagrams for a graph theory course I was taking. I plan to put in some functions to compute properties of graphs as well if I work on anything that would benefit from that.

Project page

Course Notes

These notes were transcribed in Latex during some classes I have taken. They are quickly typed live, so there may be some typos and odd formatting here and there. If you would like the .tex files and figures, you may request them over email.