Related papers: Contributions to the model theory of partial diffe…
The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory. This geometrization, in addition of giving a nice insight on this result, offers us the occasion to investigate several points of…
A Galois theory of differential fields with parameters is developed in a manner that generalizes Kolchin's theory. It is shown that all connected differential algebraic groups are Galois groups of some appropriate differential field…
An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on…
We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the…
In this paper, we establish Galois theory for partial differential systems defined over formally real differential fields with a real closed field of constants and over formally $p$-adic differential fields with a $p$-adically closed field…
We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…
We present a geometric setting for the differential Galois theory of $G$-invariant connections with parameters. As an application of some classical results on differential algebraic groups and Lie algebra bundles, we see that the Galois…
We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois…
A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and…
We prove a Galois-type correspondence between compositions of purely inseparable field extensions (including infinite ones) and subalgebras of differential operators. This correspondence can be utilized to establish a connection between…
We give a detailed proof of Kolchin's results on differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. We closely follow former works due to Pillay and…
We study the differential Galois theory of difference equations under weaker hypothesis on the field of constants of the automorphism. This framework yields a new approach to results by C.Hardouin and M.Singer, which answers possitively a…
This is a write-up of some lectures I gave in the Fall of 2021 at the Fields Institute in Toronto, as part of the Thematic Programme on Trends in Pure and Applied Model Theory. The goal of the module was to give a quick introduction to the…
Intended for mathematical physicists interested in applications of the division algebras to physics, this article highlights some of their more elegant properties with connections to the theories of Galois fields and quadratic residues.
We define vector fields, leaves and trajectories for schemes. With these tools, we are able to give a geometrical interpretation and to generalize several results of differential Galois theory and constructions on differential schemes. We…
The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of…
We prove the existence of real Picard-Vessiot extensions for real partial differential fields with real closed field of constants. We establish a Galois correspondence theorem for these Picard-Vessiot extensions and characterize real…
These are lecture notes expanding upon a set of lectures given by G.M. at the TASI 2023 School. Part I is an introduction to topological field theory, including extended topological field theory. Part II is an introduction to generalized…
In the context of differential fields of characteristic zero with several commuting derivations, we discuss the notion of $\#$-differential equations on parameterized D-torsors and their associated Galois extensions. Using model-theoretic…