We present a Galois theory of parameterized linear differential equations where the Galois
groups are linear differential algebraic groups, that is, groups of matrices whose entries are …

We investigate when a skew polynomial extension T= R [x; σ, δ] of a Hopf algebra R admits
a Hopf algebra structure, substantially generalising a theorem of Panov. When this …

Iterated Hopf Ore extensions (IHOEs) over an algebraically closed base field k of positive
characteristic p are studied. We show that every IHOE over k satisfies a polynomial identity …

Linear differential algebraic groups (LDAGs) appear as Galois groups of systems of linear
differential and difference equations with parameters. These groups measure differential …

We prove that a group definable in a model of $ ACFA $ is virtually definably embeddable in
an algebraic group. We give an improved proof of the same result for groups definable in …

We study groups defined by algebraic difference equations. These groups occur as the
Galois groups of linear differential and difference equations depending on discrete …

We study point modules of monomial algebras associated with symbolic dynamical systems,
parametrized by proalgebraic varieties which'linearize'the underlying dynamical systems …

I thank my thesis advisor Dave Marker for his help and guidance during my graduate
education. He was generous with his time and support during my time as a gradaute …

We establish several finiteness properties of groups defined by algebraic difference
equations. One of our main results is that a subgroup of the general linear group defined by …

Model Theory of Fields With Operators-a Survey. Page 107 Zoé Chatzidakis Model Theory of
Fields With Operators–a Survey For Jouko, on the occasion of his 60th birthday Abstract: This …