## Zackary Burton

**Biography**

My academic interests have always circulated between maths and physics. During high school I was under the impression that maths was just something I would be forced to do alongside my main interest physics. When I came to La Trobe University, I was still regarding physics as my major priority. The classes that, to me, sounded interesting required many maths subjects as a prerequisite. Eventually, the classes I was taking, with respect to my major, stopped requiring maths and I was given the option to choose electives completely unrelated to my interests. Regardless of this freedom, I chose every math class possible to fill my remaining classes as, in my mind; it would benefit me greatly upon higher learning within physics.

It was third year when my priorities that had previously given me a strong case of tunnel vision finally started shifting. Upon taking third year physics alongside maths, the dependence that physics had upon maths became increasingly more evident. The drive I had held in regards to physics was slowly diminishing. In my mind, there were too many beautiful explanations for simple mathematics that I just couldn’t ignore; for example, the construction of the natural numbers from the empty set. As of current, I believe mathematics to be an underlying truth to all that is. My current academic interests include group theory, geometry, lattice theory, complex analysis and universal algebra.

**Geometry of Minkowski space**

This project will first survey the classical geometry of triangles and circles in the context of the Minkowski plane. The first task here is to gain familiarity with the defining characteristics of Minkowsian geometry by seeing which of the famous theorems of Euclidean geometry (eg, nine point circle, Brianchon’s theorem, Napleon’s theorem, Morley’s miracle, etc etc) still hold in Minkowski space. It will then move on to the study of Lorentzian geometry of homogeneous manifolds of low dimension; the study of geodesics, horocycles etc. The project will enable the candidate to acquire a broader knowledge of aspects of modern differential geometry, and to learn certain computational methods using Maple. The project is designed to provide the candidate with a strong foundation for pursuing mathematical studies at a higher level.