Sachi Hashimoto

Mathematics PhD Student
Boston University
Boston, USA

Sachi Hashimoto is a mathematics PhD student at Boston University studying arithmetic geometry. She is interested in questions about rational points and explicit methods in number theory.

This work comes from a series of cyanotypes of mathematical objects. Cyanotype is an alternative photography process that creates "blueprints" of objects placed on top of light sensitized paper. Cyanotypes have a long history of use in scientific work -- Anna Atkins pioneered the cyanotype process, creating the first books of cyanotypes cataloguing algae, ferns, and other plants of the British Isles. These mathematical cyanotypes are a nod to Atkins's catalogue of botanical work.

Cursed Curve
46 x 61 cm
cyanotype on watercolor paper

This is a cyanotype of a visualization of the real locus of the split Cartan modular curve of level 13. The original visualization was made in SageMath with Kevin Carde and Jennifer Balakrishnan. Recently, Balakrishnan, Dogra, Muller, Tuitman, and Vonk developed explicit Chabauty-Kim methods which they applied to show that there are only seven rational points on this curve.