Date of Award

2021

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Graduate Group

Mathematics

First Advisor

Julia Hartmann

Abstract

Roughly speaking, the essential dimension of an algebraic object is the minimum number of parameters needed to specify the object. It was first introduced by J. Buhler and Z. Reichstein where it was used to bound the number of parameters that one may eliminate from a general polynomial by means of Tschirnhaus transformations.

In this thesis we define an analogue of essential dimension in differential algebra. As application, we show that the number of parameters in a general homogeneous linear differential equation over a field cannot be reduced via gauge transformations over the given field. We also bound the number of parameters needed to describe certain generic Picard-Vessiot extensions.

Included in

Mathematics Commons

Share

COinS