By Stéphane Gaubert
On the Solutions of Knizhnik-Zamolodchikov Differential Equations by Noncommutative Picard-Vessiot Theory
By Vincel Hoang Ngoc Minh
By Alexandros Singh
Appears in collection : Combinatorics and Arithmetic for Physics: special days
In this talk, I will use the functor of points approach to Algebraic Geometry to establish that every covariant presheaf X on the category of commutative rings — and in particular every scheme X — comes equipped “above it” with a symmetric monoidal closed category PshModX of presheaves of modules. This category PshModX defines moreover a model of intuitionistic linear logic, whose exponential modality is obtained by glueing together in an appropriate way the Sweedler dual construction on ring algebras. The purpose of this work is to explore the idea that linear logic is a logic of generalised vector bundles, in the same way as dependent type theory is understood today as a logic of spaces up to homotopy.