Student Profile: Nicholas McLean
Nicholas is a 20 year old student at The University of Adelaide studying Mathematics. Nicholas intends on completing undergraduate study in 2017, with a goal of beginning a Masters of Philosophy the year after.
Nicholas was born in Melbourne but moved to Adelaide at a young age. Nicholas attended high school at Cabra Dominican College where he was awarded DUX in 2014, along with two subject merits in mathematics and physics. Nicholas’ love for mathematics began in middle school and grew throughout high school where, by the end, he had his eyes set on pursuing further study in the area. His research interests currently include anything in the area of pure mathematics, in particular in the area of complex analysis.
Outside of university life, Nicholas tutors year 11’s and 12’s in high school mathematics, physics and chemistry as well as plays video games, specifically Call of Duty.
Chaotic Dynamics on the Riemann Sphere
Complex dynamics in one dimension is a highly active area. Of particular interest are rational functions that exhibit chaotic behaviour. The goal of this project is to come to grips with some deep results about problems in this area which can be tackled with only knowledge of undergraduate complex analysis.
Of particular interest is to develop a proof that a rational function is chaotic if its critical points are pre-periodic and to investigate the behaviour of a family of functions, and moreover find when the function behaves chaotically.