The geometry of gaussoids

Gaussoids offer a new link between combinatorics, statistics and algebraic geometry. Introduced by Lnenicka and Matus in 2007, their axioms describe conditional independence for Gaussian random variables. This lecture introduces gaussoids to an audience familiar with matroids. The role of the Grassmannian for matroids is now played by a projection of the Lagrangian Grassmannian. We discuss the classification and realizability of gaussoids, and we explore oriented gaussoids, valuated gaussoids, and the analogue to positroids. This is based on recent work with Tobias Boege, Alessio D'Ali, and Thomas Kahle.