Artists

Kathryn Lindsey

Assistant Professor

Department of Mathematics, Boston College

Chestnut Hill, Massachusetts, USA

lindseka@bc.edu

https://www2.bc.edu/kathryn-a-lindsey/

Statement

My research is in dynamical systems with connections to geometry and topology. I frequently create images, 3D objects, or interactive digital media to help gain intuition about the mathematical objects I study.

Artworks

Image for entry 'A variant of the Alexander horned sphere'

A variant of the Alexander horned sphere

20 x 25 cm

digital print on metal

2007

I created this image of a variant of the Alexander horned sphere while taking a course called "the Art and Science of Computer Graphics," taught by Duane Bailey, as an undergraduate at Williams College. The 3D set depicted here in gold is homotopic to a solid ball in 3-space; one might imagine continuously retracting the "arms" of the object and watching it shrink down to become a round ball. The complement of this set in Euclidean 3-space, however, has a much more complicated topological structure than the complement of a geometrically round ball.
Image for entry 'Ring of fire from PCF interval self-maps'

Ring of fire from PCF interval self-maps

76 x 76 cm

digital print on canvas

2017

Joint with Harrison Bray, Diana Davis, and Chenxi Wu. This plot was created using Mathematica at an AMS Mathematics Research Community program on "Dynamical Systems: Smooth, Symbolic & Measurable" as part of our joint research on the growth rates of post-critically finite interval self-maps. It is a plot of all Galois conjugates of growth rates of post-critically periodic generalized beta transformations with a growth rate in [1,2] and critical period at most 22, colored according to the critical period. The project culminated in our research paper, "The Shape of Thurston's Master Teapot" (2019, preprint on ArXiv.org).
Image for entry 'Slices of Thurston's Master Teapot'

Slices of Thurston's Master Teapot

digital video created using C++

2017

Additional info

Joint with Harrison Bray, Diana Davis and Chenxi Wu. As part of our research on Thurston's Master Teapot, we created this video to try to gain insight into the geometrical and topological properties of that set. Each frame of the video shows a 2D "slice" of the 3D set; a slice consists of Galois conjugates of growth rates of unimodal, super-attracting interval self-maps with a growth rate in a very small interval. Careful scrutiny of the video may lead one to conjecture that that points outside the unit circle (shown in white) vary continuously, while the points inside the unit circle "approximately persist"; our joint paper "The Shape of Thurston's Master Teapot" (2018) proves this result.