Dear all, Thomas Seiller (CNRS) will give a talk for this month's PCT seminar (https://pctseminar.github.io/<https://pctseminar.github.io>) on Friday June 5 at 10am JST/11am AED (1am UTC). The zoom link to join the seminar is: https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1<https://kyoto-u-edu.zoom.us/j/82401794000?pwd=VjVmzVjmlgxhkdHES4xYeQBTpMzQkS.1> Title: From Statistical Data to Geometry and Logic via Isbell Nuclei Abstract: The impressive results obtained by generative language models suggest that statistical information contained in a sufficiently large corpus can be used to recover significant linguistic structure. In particular, Levy and Goldberg (2014) showed that word embeddings can be recovered from low-rank factorisations of word co-occurrence matrices, as obtained in practice through singular value decomposition. While this provides an important first step towards understanding mathematically the structure exploited by language models, it remains limited, notably in its treatment of compositionality. In this talk I will present a categorical refinement of this perspective, drawing on enriched category theory and realisability methods for linear logic. Starting from a real-valued measure (M:C\times D\to\mathbb R), one studies the Isbell nucleus of the induced enriched adjunction. This construction simultaneously generalises classical formal concepts defined from binary relations and singular value decomposition of linear operators. While every nucleus carries a canonical lattice structure, in the statistical setting this is only part of a considerably richer picture. On the one hand, the nucleus admits a tropical geometric structure, with row and column spaces appearing as dual presentations of the same object, equipped with a canonical projective metric and polyhedral decomposition. On the other hand, when the underlying data is additionally equipped with concatenation, it carries a type-theoretic structure arising from linear realisability and closely related to substructural logics. We hope to see you there! If you cannot make it, talks after posted on youtube afterwards: https://www.youtube.com/@PCTSeminar Best wishes, Soichiro Fujii, Zeinab Galal, JS Lemay