91社区

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

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

COMMITTEE MEMBERS

Chair
David A. Stephens, Professor,聽Department of聽Mathematics and Statistics, 91社区

Supervisors
Niky Kamran, Professor,聽Department of聽Mathematics and Statistics, 91社区
Vestislav Apostolov, Professor,聽D茅partement de math茅matiques,聽Universit茅 du Qu茅bec 脿 Montr茅al聽

Internal Examiner
Jaques Hurtubise, Professor, Mathematics and Statistics, 91社区

External Member
Alexander Maloney, Associate Professor of Physics, Department of Physics, 91社区

Pro-Dean
TBA

ABSTRACT

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