Beyond the g-Conjecture in Combinatorial Mathematics

Explore a mathematical seminar that delves into McMullen's g-conjecture, one of the most significant problems in combinatorics over the past half-century. Learn about the complete characterization of i-dimensional faces in sphere triangulation and discover the groundbreaking 2020 proof by Papadakis and Petrotou involving anisotropy of quadratic forms in characteristic 2. Follow along as the historical context and key concepts behind the conjecture's proof are examined, including recent collaborative developments with Matt Larson, Isabella Novik, and Kalle Karu. The hour-long presentation at the Institute for Advanced Study provides an in-depth look at this fundamental mathematical concept and its ongoing implications in the field.