The paper "Degenerate Kalman filter error covariances and their convergence onto the unstable subspace" has been accepted by the Journal of Uncertainty Quantification (SIAM/ASA JUQ). Karthik Gurumoorthy, Amit Apte, Alberto Carrassi, Colin Grudzien, and Chris Jones are co-authors. This is my first paper in a maths journal! The preprint is available here. The paper rigorously describes the implication of the dynamics of a chaotic model on the error covariance matrix of a (ensemble) Kalman filter applied to this model. In particular, the paper quantitatively describes how the error covariance matrix projects and stays confined to the unstable and neutral subspace of the dynamics. This mathematically justifies the paradigm know as AUS (assimilation in the unstable subspace) put forward over the past ten years by Anna Trevisan and co-authors.