Trent Skorka has recently graduated from a Mathematics degree at the University of Queensland and will be commencing Honours this year. Even from school, where he studied Mathematics B and C, and Physics, he has expressed strong interest in differential equations and mathematical physics. He is still exploring research and other areas of mathematics before considering a specific field for a future profession.
After completing his Bachelor degree in 2014, Trent was offered a Summer Research Scholarship by the University of Queensland under the supervision of Dr Phillip Isaac. This research aimed to investigate Lie symmetry algebras of differential equations, as previously examined by Dobrev et al with regards to the so-called Schrodinger algebra. Little is known of the general theory of irreducible representations of this algebra. Results from the present study, as well as more recent research, will contribute to the application of these techniques to other systems of physical interest.
In addition to this research, Trent will also be completing his Honours thesis around the control of predator-prey systems. He has chosen to study two different fields of mathematics to allow for a more diverse understanding of the areas he may pursue in the future.
Lie symmetries of differential equations
Symmetry methods are particularly useful for solving differential equations and investigating properties of their solutions. In this project, we will study applications of Lie symmetry methods to a range of differential relations. The focus will be on applications such as conservation laws and classically integrable systems, with an aim both to obtain explicit solutions, and qualitative statements on properties of solutions. Specifically, we will look at symmetries of the Schrodinger equation, and recent generalisations to l-conformal Galilei algebras.