I am a PhD student in the School of Mathematics and Statistics at the University of Sydney. I am currently studying the PainlevĂ© equations (both continuous and discrete) under the supervision of Prof. Nalini Joshi. I study the behaviours of these equations by using the method of asymptotics, in particular the method of averaging. I am also interested in the special solutions of discrete and continuous PainlevĂ© equations, the associated problem (ie the isomonodromy deformation method), as well as the geometry behind these.

I completed my honours degree in 2012, supervised by Prof. Nalini Joshi, studying Darboux transformation on nonlinear differential equations.

f(x,y)=(x^4 + y^4 - x^2 - y^2)^2-9 x^2 y^2, an algebraic curve with 5 ordinary
singularities at (0,1), (0,-1), (1,0), (-1,0) and (0,0).

Invariant for autonomous q-PIII

K(x,y)= (x^2 y^2 - (c + d) x y (x + y) + c d (x^2 + y^2) - (a + b) c d (x +y) + a b c d)/(x
y) is the invariant for autonomous q-PIII.
The following pictures show all 8 base points
in P^1 x P^1 and potential duplicates as well.

Invariant curve for autonomous q-PIII in complex projective space

Second invariant curve for autonomous q-PIII in complex projective space

Initial value space of autonomous q-PIII, wlog, we assume that b>a and d>c. D_i, i=1,2,3,4 are the divisors.

An algebraic curve with 5 ordinary singularities at (0,1), (0,-1), (1,0), (-1,0) and (0,0).