Algebra Commons^™

Topics In Gravitational Wave Physics, Aaron David Johnson

Graduate Theses and Dissertations

We begin with a brief introduction to gravitational waves. Next we look into the origin of the Chandrasekhar transformations between the different equations found by perturbing a Schwarzschild black hole. Some of the relationships turn out to be Darboux transformations. Then we turn to GW150914, the first detected black hole binary system, to see if the nonlinear memory might be detectable by current and future detectors. Finally, we develop an updated code for computing equatorial extreme mass ratio inspirals which will be open sourced as soon as it has been generalized for arbitrary inclinations.

Families Of Homogeneous Licci Ideals, Jesse Keyton

Graduate Theses and Dissertations

This thesis is concered with the graded structure of homogeneous CI-liaison. Given two homogeneous ideals in the same linkage class, we want to understand the ways in which you can link from one ideal to the other. We also use homogeneous linkage to study the socles and Hilbert functions of Artinian monomial ideals.

First, we build off the work of C. Huneke and B. Ulrich on monomial liaison. They provided an algorithm to check the licci property of Artinian monomial ideals and we use their method to characterize when two Artinian monomial ideals can be linked by monomial regular sequences. …