James Geelen

Subject: Prospective PhD student Dear Professor Geelen, My name is [your name], and I am a [your current degree or role] at [your institution]. I am applying for a PhD position starting in [term and year]. I read your paper "OpenAI's proof of the Cycle Double Cover Theorem" (2026), and it connects closely to my own work on [your research topic]. [One or two sentences on what you did and what you learned.] Are you accepting new PhD students for [term and year]? I have attached my CV and transcripts, and I would be glad to talk at a time that suits you. Thank you for your time. Kind regards, [your name]