The preprint "Families of polytopes with rational linear precision in higher dimensions" by Isobel Davies, Eliana Duarte, Irem Portakal and Miruna-Stefana Sorea has been recently uploaded to the arXiv!
Link to the paper: arXiv:2109.08151
In this article we introduce a new family of lattice polytopes with rational linear precision. For this purpose, we define a new class of discrete statistical models that we call multinomial staged tree models. We prove that these models have rational maximum likelihood estimators (MLE) and give a criterion for these models to be log-linear. Our main result is then obtained by applying Garcia-Puente and Sottile's theorem that establishes a correspondence between polytopes with rational linear precision and log-linear models with rational MLE. Throughout this article we also study the interplay between the primitive collections of the normal fan of a polytope with rational linear precision and the shape of the Horn matrix of its corresponding statistical model. Finally, we investigate lattice polytopes arising from toric multinomial staged tree models, in terms of the combinatorics of their tree representations.
In a few weeks, some members of our group will participate in the kick-off meeting of the 2nd phase of the Priority Programme "Geometry at Infinity" (SPP2026) of the German Research Foundation (DFG).
The SPP2026 funds many research groups across Germany (including us!) working on various subareas of geometry, topology, analysis and group theory.
See you there!