Special Year Seminar II

The conjecture in combinatorics that has received perhaps the most attention over the last 50 years is McMullen's g-conjecture. It provides a complete characterisation of the number of $i$-dimensional faces in a triangulation of an $(d - 1)$-dimensional sphere for $0 \le i \le d - 1$. An extremely novel proof was given in 2020 by Papadakis and Petrotou involving anisotropy of quadratic forms in characteristic $2$. We'll survey some of the history and ideas behind the proof of the conjecture, and then discuss recent work with Matt Larson, Isabella Novik and Kalle Karu.