Title: On High Girth Steiner-Triple Systems and Subspace Designs

Abstract: We discuss the recent resolutions of the 1973 conjecture of Erdős on the existence of high girth Steiner triple systems and the existence of subspace designs. The talk will focus on placing these results within the context of classical design theory and within recent advances in the absorption method in combinatorics.
Based on joint works w. Peter Keevash, Matthew Kwan, Ashwin Sah, and Michael Simkin