Euler Circle

In the summer of 2026 I was an apprentice in Euler Circle's independent research and paper writing programme, working under Dr. Simon Rubinstein-Salzedo. I was accepted on 13 April, and the class ran from 8 June to 10 July: guest lectures and paper-writing talks on Mondays and Thursdays, and project work with a teaching assistant on Tuesdays and Fridays.

I wrote a 16-page expository paper on chromatic roots, “How Close Can a Chromatic Root Get to One?”, which is published on Expositio, and presented it to more than 40 attendees. In it I proved that no chromatic root lies below 0, in (0, 1), or in (1, 32/27]. The proof-writing practice from PACT carried straight into it.