Akito Koike
Slices in Schottky space
Fractal curves on the plane can be obtained as limit sets of the so-called Schottky groups. These are groups of non-singular complex matrices acting as fractional linear transformations on the Riemann sphere. The Hausdorff dimension of the associated fractal is intimately associated with the geometry and algebra of the corresponding Schottky group. Coarse properties of the space of all Schottky groups are well understood since the 1970s through work of Jorgensen, Marden and Maskit. Recent theoretical and computational advances allow a finer study of Schottky space, and helped understand the groups and limit sets associated with two 2-dimensional slices in the 6-dimensional space of space of all 2-generator Schottky groups. This project applies new tools to systematically analyse new slices in the space of all 2-generator Schottky groups and use them to address open problems in the field.
Akito Koike
The University of Sydney
Akito is an undergraduate student at the University of Sydney, completing a Bachelor of Science and Advanced Studies, majoring in mathematics and physics. He enjoys and appreciates a wide variety of topics within mathematics, such as for example, number theory, complex analysis and statistics. His main interests lie in abstract algebra, such as algebraic topology and representation theory, and plans to pursue an honours in pure mathematics, with a project based in algebra.
Outside of mathematics, Akito enjoys learning about the universe through physics, especially quantum physics. His hobbies also include playing chess, speedsolving Rubik’s cubes, and sailing.
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