Closed graph theorems for bornological spaces

The aim of this paper is that of discussing Closed Graph Theorems for bornological vector spaces in a way which is accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over $\mathbb{R}$ and $\mathbb{C}$ to deduce Closed Graph Theorems for bornological vector spaces over any complete, non-trivially valued field, hence encompassing the non-Archimedean case too. We will end this survey by discussing some applications. In particular, we will prove de Wilde's Theorem for non-Archimedean locally convex spaces and then deduce some results about the automatic boundedness of algebra morphisms for a class of bornological algebras of interest in analytic geometry, both Archimedean (complex analytic geometry) and non-Archimedean

Analytic geometry over F_1 and the Fargues-Fontaine curve

This paper develops a theory of analytic geometry over the field with one element. The approach used is the analytic counter-part of the Toen-Vaquie theory of schemes over F_1, i.e. the base category relative to which we work out our theory is the category of sets endowed with norms (or families of norms). Base change functors to analytic spaces over Banach rings are studied and the basic spaces of analytic geometry (like polydisks) are recovered as a base change of analytic spaces over F_1. We end by discussing some applications of our theory to the theory of the Fargues-Fontaine curve and to the ring Witt vectors.Comment: Small corrections have been made in the last section of the paper and some typos have been correcte

Dagger Geometry As Banach Algebraic Geometry

In this article, we apply the approach of relative algebraic geometry towards analytic geometry to the category of bornological and Ind-Banach spaces (non-Archimedean or not). We are able to recast the theory of Grosse-Kl\"onne dagger affinoid domains with their weak G-topology in this new language. We prove an abstract recognition principle for the generators of their standard topology (the morphisms appearing in the covers). We end with a sketch of an emerging theory of dagger affinoid spaces over the integers, or any Banach ring, where we can see the Archimedean and non-Archimedean worlds coming together

On the uniqueness of invariant states

Given an abelian group G endowed with a T-pre-symplectic form, we assign to it a symplectic twisted group *-algebra W_G and then we provide criteria for the uniqueness of states invariant under the ergodic action of the symplectic group of automorphism. As an application, we discuss the notion of natural states in quantum abelian Chern-Simons theory.Comment: 29 pages -- accepted in Advances in Mathematic

Pensar la Universidad desde Latinoamérica: un desafío pedagógico en construcción

El artículo focaliza el lugar de la Universidad en la formación de una ciudadanía democrática en el contexto latinoamericano en el marco de los 100 años de la Reforma Universitaria y desde los aportes del proyecto de investigación sobre Teorías Pedagógicas en prácticas democráticas en las instituciones educativas.Fil: Bambozzi, Enrique. Universidad Nacional de Córdoba. Facultad de Ciencias de la Comunicación; Argentina.Educación General (incluye capacitación, pedagogía y didáctica