Ph.D. Oral Defense - Kael Dixon

The Department of Mathematics and Statistics invites you to attend the Ph.D. Oral Defense of Mr. Kael Dixon

THESIS TITLE: Completions of regular ambitoric 4-manifolds: Riemannian Kerr metrics and beyond

COMMITTEE MEMBERS

Chair
David A. Stephens, Professor, Department of Mathematics and Statistics, McGill University

Supervisors
Niky Kamran, Professor, Department of Mathematics and Statistics, McGill University
Vestislav Apostolov, Professor, Département de mathématiques, Université du Québec à Montréal 

Internal Examiner
Jaques Hurtubise, Professor, Mathematics and Statistics, McGill University

External Member
Alexander Maloney, Associate Professor of Physics, Department of Physics, McGill University

Pro-Dean
TBA

ABSTRACT

We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex near the singularity corresponding to the ring singularity in the interior of the black hole. We also study the Tomimatsu-Sato metrics, whichgeneralize the Kerr metrics. We show that these also admit Riemannian signature analogues, and admit almost-complex analogues of ambitoric structures. We then proceed to classify regular ambitoric 4-orbifolds with some completeness assumptions. The tools developed also allow us to prove a partial classi cation of ompact Riemannian 4-manifolds which admit a Killing 2-form.