Tracey Balehowsky, BSc (Hon.), MSc, PhD

Tracey Balehowsky. They have dark hair and wear glasses.

Areas of Research

Geometric inverse problems
In such problems I often look for what geometric information on (pseudo-) Riemannian manifolds one can use to determine the metric. See papers and for example of my work on such problems.
Transformation optics and cloaking
In these problems one is looking to mathematically model the construction a device (called a cloaking device) which distorts optical waves to render an object invisible to an observer. In particular, I have looked at a use case for such a device for modelling the optical properties of manifolds which represent a geometric configuration for our universe. See for an example of such a problem.
Geometric flows
Geometric flows are PDEs which describe how a shape (a (pseudo-) Riemannian manifold) can be deformed according to some aspect of the geometric. Such flows include mean curvature flow (MCF) and Ricci flow. I am particularly interested in studying MCF and Ricci flow as they appear in related geometric or physical questions. See and for examples.
Particle kinematics
Particle kinematics can be modelled by a Boltzmann equation, which describes particle motion and accounts for interactions between particles, such as particle collisions and particle evaporation. I have studied such an equation from a theoretical inverse problem perspective (see and from an applied atmospheric science perspective (see I would be happy to supervise a thesis related to these research avenues.

Supervising degrees

Math and Statistics - Masters: Seeking Students
Math and Statistics - Doctoral: Seeking Students