

Geometrical finiteness in strictly convex projective geometry
By Pierre-Louis Blayac


Local minimization of fuzziness under high symmetry
By Franco Vargas Pallete


The shape of the limit cone for positive representations
By Jeffrey Danciger
Appears in collection : 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics
After recalling the categorical axioms of local quantum field theory à la Reshetikhin, and verifying that quantum mechanics constitutes an instance of it, we will introduce its subsector consisting of models whose time-dependence admits a complexification to a complex curve. Under genericity assumptions, we will show how the moduli description of Boalch, and a twist of the Biswas-Hurtubise canonical kernel, provide the sought restricted categorical formulation. We will conclude by mentioning the new perspective this offers on quantum dynamics.