My research area is Integrable Systems and Painlevé equations. Since 2013, I have been part of the research group of Prof. Nalini Joshi.
I majored in Physics and Mathematics at the University of Sydney. After completing my Honours year doing a project in the High Energy Physics Group at the School of Physics, I decided to do my PhD with Prof. Joshi on the Painlevé equations. The reason for this choice is that the Painlevé equations are highly relevant in physics and many areas of science. However, later I also learnt that they are extremely interesting in their own right and possess many beautiful properties.
Recently, I have been working on the connections of different classes of integrable systems, exploiting the geometric/combinatorial properties of the Weyl group symmetries of integrable equations. This involves interpreting systems of integrable equations as the higher dimensional regular polytopes and lattices of the Weyl groups.
- Coxeter groups
- Combinatorial geometry
- Mathematical physics (exactly solvable models)
- Painlevé equations
- Lax pairs and monodromy problem
- Special continuous and discrete functions
- Integrable quad-equations
Joshi, N., Nakazono, N.; Shi, Y. (2016) Lattice equations arising from discrete Painlevé systems II. A4(1) case. Journal of Physics A. Mathematical and Theoretical. 49: 495201.
Joshi, N., Nakazono, N.; Shi, Y. (2016) Reflection groups and discrete integrable systems. Journal of Integrable Systems, 1(1), 1-37.
Hay, M., Howes, P., Nakazono, N. and Shi, Y. (2015) A systematic approach to reductions of type-Q ABS equations. Journal of Physics A: Mathematical and Theoretical, 48: 095201.
Joshi, N., Nakazono, N. and Shi, Y. (2014) Geometric Reductions of ABS equations on an n-cube to discrete Painlevé systems. Journal of Physics A: Mathematical and Theoretical, 47: 505201.
Joshi, N., Shi, Y. (2012) Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: II. Hypergeometric Solutions. Proceedings of Royal Society Series A, 468: 3247-3264.
Joshi, N., Shi, Y. (2011) Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational Solutions. Proceedings of Royal Society Series A, 467: 3443-3468.
TRAVEL IN 2016
June/July: ASIDE and SIDE12 Symmetries and Integrability of Difference Equations conference in Montréal, Canada
April: DISW2016 (Discrete Integrable Systems Workshop) in Sanya, China