Yang Shi

Yang Shi by Ted SealeyI am a Postdoctoral Research Assistant in the School of Mathematics and Statistics at the University of Sydney.

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.

Research
  • Coxeter groups
  • Combinatorial geometry
  • Mathematical physics (exactly solvable models)
  • Painlevé equations
  • Lax pairs and monodromy problem
  • Special continuous and discrete functions
  • Integrable quad-equations
Circle pattern corresponding to the discrete analogue of holomorphic functions z^(4/5).
Circle pattern corresponding to the discrete analogue
of holomorphic functions z^(4/5).
Recent Publications

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 systemsJournal of Integrable Systems1(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 systemsJournal of Physics A: Mathematical and Theoretical47: 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 A468: 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 A467: 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

Contact

yang.shi@sydney.edu.au

5-cube
Orthogonal projection of 5-dimensional hypercube in 2D
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