About Professor Nalini Joshi

I am interested in the mathematical analysis of non-linear systems, in particular, in developing new methods of analysing and deducing the special properties of integrable systems which have astonishingly beautiful behaviours.

Interest in non-linear models has grown dramatically over the last four decades, since, on the one hand, chaos was discovered in simple models of the atmospheric circulation (e.g., in the well-known Lorenz equations), and on the other hand astonishingly well-ordered and predictable behaviour was found in certain models of non-linear lattices used to describe thermal properties of metals (e.g. the FPU lattice and the Korteweg-de Vries equation). The latter observations led to the theory of solitons and completely integrable systems, one of the most profound advances of twentieth century mathematics. Reductions of soliton equations led to the Painlevé equations, which are canonical representations of integrable models in one dimension. Integrable systems have now been recognized as widely applicable models of science, occurring in fluid dynamics, particle physics, solid state physics, optics and many other fields. My research has focussed on methods to describe solutions of such systems.

Nalini Joshi holds a PhD and MA from Princeton University in Applied Mathematics and a BSc (Hons) from the University of Sydney. She has held lecturing positions and fellowships at ANU, UNSW, and the University of Adelaide, as well as visiting positions at institutions including Princeton, Kyoto, Manchester and the Isaac Newton Institute of Mathematical Sciences at Cambridge University. In 2002, she returned to the University of Sydney to take up the Chair of Applied Mathematics and became the first female mathematician to hold a Chair there. She was awarded the Georgina Sweet Australian Laureate Fellowship in 2012.

Selected publications

1. Atkinson J, Joshi N. Singular-Boundary Reductions of Type-Q ABS Equations, International Mathematics Research Notices, 24 (2012), 31 pages.2. Atkinson J, Joshi N. The Schwarzian variable associated with discrete KdV-type equations, Nonlinearity, 25 (2012), 1851–1866.3. Joshi N, Shi Y. Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468 (2012), no. 2146, 9.4. Joshi N, Shi Y. Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutions, Proceedings of the Royal Society A, 467 (2011), 3443–3468.5. Duistermaat JJ, Joshi N. Okamoto's Space for the First Painlevé Equation in Boutroux Coordinates, Archive for Rational Mechanics and Analysis, 202 (2011), no. 3, 707–785.6. Kassotakis P, Joshi N. Integrable Non-QRT Mappings of the Plane, Letters in mathematical physics, 91 (2010), no. 1, 71–81. MR25773008. Ramani A, Grammaticos B, Joshi N. Second-degree discrete Painlevé equations conceal first-degree ones, Journal of Physics A: Mathematical and Theoretical, 43 (2010), 175207 (9pp).9. Butler S, Joshi N. An inverse scattering transform for the lattice potential KdV equation, Inverse Problems, 26 (2010), 28 pages.