Related papers: Completeness classes in algebraic complexity theor…

Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps.…

We study group algebras for compact groups in the category of real and complex weakly complete vector spaces. We also show that the group algebra is a quotient of the weakly complete universal enveloping algebra of the Lie algebra of the…

We consider the problem of characterizing derived endomorphism algebras of simple objects in length categories up to quasi-isomorphism. We give such a characterization for module categories, abelian categories, exact categories, as well as,…

We analyse some aspects of the notion of algebraic exponentiation introduced by the second author [16] and satisfied by the category of groups. We show how this notion provides a new approach to the categorical-algebraic question of the…

We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.

We discuss the complexity of completions of partial combinatory algebras, in particular of Kleene's first model. Various completions of this model exist in the literature, but all of them have high complexity. We show that although there do…

These notes form an extended version of a minicourse delivered in Universite de Montreal (June 2002) within the framework of a NATO workshop ``Normal Forms, Bifurcations and Finiteness Problems in Differential Equations''. The focus is on…

We introduce a class of strongly \'{e}tale difference algebras, whose role in the study of difference equations is analogous to the role of \'{e}tale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's…

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.

We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…

We develop theory concerning non-uniform complexity in a setting in which the notion of single-pass instruction sequence considered in program algebra is the central notion. We define counterparts of the complexity classes P/poly and…

This is a introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of their interrelations.

The paper "Is Complexity an Illusion?" (Bennett, 2024) provides a formalism for complexity, learning, inference, and generalization, and introduces a formal definition for a "policy". This reply shows that correct policies do not exist for…

This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…

A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing $k-$summability theory as developed by J.-P. Ramis. Departing from a strongly regular sequence of positive…

This text has two parts; the first is the essentially unmodified text of the 1973-74 seminar of M. Lejeune-Jalabert and B. Teissier on integral dependence in complex analytic geometry with J-J. Risler's appendix on the Lojasiewicz exponents…

This article surveys recent advances in applying algebraic techniques to constraint satisfaction problems.

We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…

Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…