My name is Timothy Buttsworth. I have just completed my second year of the Bachelor of Science at UQ. I study Mathematics with the UQ School of Mathematics and Physics. I received a Dean’s commendation for excellence in Semester 1 2013, and Semester 1 2014. I am interested in functional analysis and geometric analysis. In particular, I am interested in the Ricci Flow, and my research this summer will be in this area.
Riemannian Metrics on Doubled Manifolds
A differentiable manifold is an object that generalises the concepts of curves and surfaces and plays important roles in many areas of mathematics and physics. To study the shape of a manifold, one uses Riemannian metrics. Finding suitably well-behaved metrics is of fundamental interest in geometry. The Ricci Flow is an important tool for constructing these metrics. We will explore results about the Ricci Flow for manifolds with boundary (i.e., with edges) by exploiting the doubling technique.