Professor Nalini Joshi
FAA
F07  Carslaw Building
The University of Sydney
Telephone  9351 2172 
Fax  9351 4534 


Website 
Personal web page 
Biographical details
Nalini Joshi is a Georgina Sweet Australian Laureate Fellow in mathematics at the University of Sydney. She develops mathematical methods to study solutions of integrable systems, which arise as universal models in physics, such as the Painleve equations.
She obtained her PhD from Princeton University and has held the Chair of Applied Mathematics at the University of Sydney since 2002.
Research interests
Nalini's research interests lie in nonlinear differential and difference equations, with a particular focus on asymptotic methods. Currently, Nalini is creating a geometric framework to reveal properties of critical solutions of nonlinear models that reflect universal structures in physical models.
Nonlinear integrable systems arise in a wide variety of fields, including ion channel transport in biology, random matrix theory, string theory and orthogonal polynomial theory. Many such systems appear as universal mathematical models in certain contexts. In the case of one continuous dimension, the systems of interest are called the Painlevé equations, while in two or more dimensions, the equations are soliton equations.
Their discrete versions have been at the leading edge of developments in recent times. However, the emphasis in the field has been focused on the identification of integrable discrete versions of the Painlevé equations and soliton equations. These equations provide an insight into physical models, such as random matrix theory. However, our knowledge of their solutions remains extremely limited.
One major problem in this field lies in the fact that the mathematical tools used widely to analyse differential equations are not available for analysing discrete equations. One way (possibly the only way) to overcome this problem is to analyse solutions as functions of initial values. Duistermaat and Joshi (J. J. Duistermaat and N. Joshi, “Okamoto's Space for the First Painlevé Equation in Boutroux Coordinates”, Archive for Rational Mechanics and Analysis, 202 (2011), 707785) showed how to analyse solutions of the first Painlevé equation in the space of its initial values. This approach connected the analytic properties of solutions to properties of algebraic curves that they parametrize, for the first time in the field of integrable systems.
Specific research areas: Integrable systems, the Painlevé equations, geometric asymptotics, nonlinear dynamics, slowfast systems, nonlinear waves, chaos, perturbation theory
Teaching and supervision
See Nalini's course on integrable systems. Nalini is currently supervising several PhD projects in this area, which propose to extend the mathematical toolbox to describe solutions of nonlinear differential and discrete equations.
Awards and honours
Fellow of the Australian Academy of Science (elected 2008)
International links
(The University of Leeds)
I collaborate with Professor Frank W. Nijhoff, who is the Professor of Mathematical Physics. Currently, I am cowriting a book with him and Professor Jarmo Hietarinta from the University of Turku in Finland. 

(The University of Leeds)
Visiting Professor 
Selected grants
2013
 Critical solutions of nonlinear systems; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
2012
 Geometric construction of critical solutions of nonlinear systems; Joshi N; Australian Research Council (ARC)/Australian Laureate Fellowships (FL).
2011
 Geometry and Analysis of Discrete Integrable Systems; Dullin H, Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
2010
 Random and integrable models in mathematical physics (RIMMP); Grava T, Klein C, Joshi N; European Commission (Belgium)/Marie Curie Action: International Research Staff Exchange (IRSES).
2009
 Integrable Lattice Equations; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
2008
 Integrable Lattice Equations; Joshi N; University of Sydney/Bridging Support.
2006
 New Directions in Nonlinear Mathematical Asymptotics; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
2005
 Integrable functional and delay differential equations; Cosgrove C, Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
2003
 Mathematical biosciences network; Joshi N; Australian Research Council (ARC)/Special Research Initiatives (SRI).
 Global Behaviour of Integrable Complex Systems; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
2002
 Singularities And Classifications Of Integrable Systems; Joshi N, Cosgrove C; Australian Research Council (ARC)/Discovery Projects (DP).
1997
 Asymptotics and integrability of nonlinear differential and difference equations; Joshi N; Australian Research Council (ARC)/Australian Senior Research Fellowship.
Selected publications

































