In-Person Talk

In this talk I'll discuss our recent resolution of a conjecture due to Erdős on the existence of Steiner triple systems with arbitrarily high girth. I'll start by giving a brief overview of random greedy processes and the method of iterative absorption, and discussing the relevant challenges in the high-girth setting. Then, I'll outline some ideas that help overcome these challenges, related to sparsification, efficient absorption, and "retrospective" analysis of random processes. This is joint work with Ashwin Sah, Mehtaab Sawhney, and Michael Simkin.