Alexander Stokes is a fourth year student at the University of Sydney studying towards a Bachelor of Science (Advanced Mathematics) and Bachelor of Arts. His main research interests so far have been applications of algebra and geometry to the study of dynamical systems, in particular the Painlevé equations and other integrable systems. He lived in Japan as a child and is majoring in Japanese studies alongside mathematics and it was initially the connection to Japan, where much important work has been done in this area, that drew him to it.
Alexander later realised, however, that this is a very diverse field in which the combination of many exotic areas of pure maths leads to beautiful insights into systems that exhibit behaviour that is too remarkable to be coincidence. He spent the first semester of 2015 at University College London, during which time he took several courses in algebra, Riemannian geometry and the connections between them, which he hopes to explore further in the future and perhaps apply to Integrable Systems when he proceeds to Honours in 2016.
Outside of maths his interests are varied but have much the same focus on the beauty of thinking. As part of his arts degree he studied electroacoustic and computer music at the Sydney Conservatorium and is very excited by the prospect of links between the worlds of maths, music and art.
Symmetry Analysis Of Pole Distribution Of Special Solutions Of The Continuous/Discrete Painleve Equations
The aim of this project is to give a qualitative description of the zero distributions of a class of very important polynomials arising as special solutions of the Painlevé transcendents. Some recent numerical study have shown that the zero distributions are “lattice like” and highly structured. On the other hand, Painlevé equations are shown to have affine Weyl group symmetries. The natural question to ask: can we describe the geometry of the locations of the zeros using the affine Weyl symmetry of the Painlevé equations?