Random Monomial Ideals - Seminar on Applied Geometry and Algebra

Explore the fascinating world of random monomial ideals in this 46-minute seminar presented by Sonja Petrović from the Illinois Institute of Technology. Delve into a collaborative study that draws inspiration from random graphs and simplicial complexes, aiming to understand the average behavior of ideals. Discover proven theorems about probability distributions, expectations, and thresholds for events involving monomial ideals with specific properties. Examine experimentally-backed conjectures on regularity, projective dimension, strong genericity, and Cohen Macaulayness of random monomial ideals. Learn how these models can be applied to generate other algebraic objects and prove the existence of desired properties. Gain insights into ongoing research in this field, moderated by Jose Israel Rodriguez from the University of Wisconsin, Madison.