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


Website 
Personal web page 
Biographical details
PayneScott Professor Nalini Joshi AO is Chair of Applied Mathematics at the University of Sydney, and a Georgina Sweet Australian Laureate Fellow.
Nalini was born and spent her early childhood in Burma, before her family emigrated to Australia. She was awarded a BSc (Hons), with the University Medal in applied mathematics, by the University of Sydney and then a PhD in computational and applied mathematics by Princeton University in the USA.
Her research focuses on mathematical methods to study integrable systems, which arise as universal models everywhere. Nalini's strong research achievements led to several distinctions. She was elected as a Fellow of the Australian Academy of Science in 2008, won an Australian Research Council Georgina Sweet Australian Laureate Fellowship in 2012 and was the 150th AnniversaryHardy Fellow of the London Mathematical Society in 2015.
Nalini also has a keen intereset in diversity and her Laureate Fellowship had a component to attract and retain female researchers in STEM. She was foundation coChair of the SAGE (Science in Australia Gender Equity) national initiative, which is currently running a pilot program that involves 44 research organisations in Australia, including 33 universities.
In the 2016 Queen’s Birthday honours, Nalini was appointed an Officer of the Order of Australia for distinguished service to mathematical science and tertiary education as an academic, author and researcher, to professional societies, and as a role model and mentor of young mathematicians.
Research interests
Nalini's research focuses on ways to describe new special functions that arise as models in large classes of applications.
If each function was a number, they would be like the transcendental number π, which cannot be expressed as a finite combination of simpler numbers, yet they appear everywhere in applications.
These special, universal functions describe a wide range of pheneomena, including:
 the distribution of large prime numbers;
 collisions of atomic particles;
 aircraft boarding times;
 bus arrival times;
 the New York subway system;
 electric fields in electrolyte solutions;
 magnetic fields and waves in plasma physics;
 water waves in the oceans;
 stationary solutions of Einstein’s equations of general relativity;
 cloud formations in the atmosphere.
Nalini describes her research as developing methods to solve mathematical puzzles that allow her to discover and describethese functions. The puzzles involve nonlinear differential and difference equations, studied through a wide variety of lenses: including analysis, algebra, algebraic geometry, topology, and asymptotic methods in limits.
The equations she studies are called integrable systems. When they involve one independent variable, they are the Painlevé equations, while in two or more variables, the equations are soliton equations.
The mathematical tools involve a panorama of different perspectives. Instead of describing solutions as functions of an independent variable like time, they can be tracked by curves that go through initial values. The first perspective is like pointing a telescope to one point in the sky at night and taking pictures while time is changing. The second perspective is like tracking one star as it follows circular arcs of light in the sky at night.
The second perspective is called a space of initial values. It turns out that the geometry of this space gives us a great deal of information about the global nature of all possible solutions of the integrable systems and leads to some deep algebraic descriptions of the solutions, given by reflection groups.
The discrete Painlevé equations turn out to be given by translations (or walks) on lattices created by affine reflection groups. The results are very pretty and beautiful.
Nalini's research papers and books can be found on her publication page or her OrCiD page.
Specific research areas: Integrable systems, the Painlevé equations, discrete Painlevé equations, lattice equations, geometric asymptotics, nonlinear dynamics, nonlinear waves, perturbation theory.
Teaching and supervision
See Nalini's course on integrable systems. Nalini has several open PhD projects in this area, which propose to extend the mathematical toolbox to describe solutions of nonlinear differential and discrete equations.
Timetable
N_Joshi
Awards and honours
Fellow of the Australian Academy of Science (elected 2008)
ARC Georgina Sweet Australian Laureate Fellowship (201218)
AFR Westpac 100 Women of Influence (2016)
PayneScott Professorial Distinction (2016)
Eureka award for Outstanding Mentor of Young Researchers (2018)
In the media
 Interview with Charlie Pickering on the Weeklyhttps://www.youtube.com/watch?reload=9&v=I7MAdUPGhQ
 Answering a question about time travel on ABC Q&A with Professor Brian Coxhttps://www.abc.net.au/news/20141020/istimetravelpossibletwoscientistsgivetheirviewsonqanda/5828532
International links
(University of Kyushu)
I hold an Australian Research Council grant with Professor Kenji Kajiwara, who is a member of the Centre for Mathematics in Industry, University of Kyushu. 

(The University of Leeds)
I collaborate with Professor Frank W. Nijhoff, who is the Professor of Mathematical Physics. Our recent book ``Discrete Systems and Integrability'', coauthored together with Professor Jarmo Hietarinta from the University of Turku in Finland, was published by Cambridge University Press. 

(The University of Leeds)
Visiting Professor 
Selected grants
2016
 Reflection Groups and Discrete Dynamical Systems; Joshi N, Kajiwara K; Australian Research Council (ARC)/Discovery Projects (DP).
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).
 A national disciplinespecific professional development programme for lecturers and tutors in the ma; Bower M, Vu T, Bloom W, Donovan D, Brown N, Skalicky J, L'och B, Joshi N, Wood L; Australian Learning and Teaching Council/Leadership for Excellence.
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
 Global Behaviour of Integrable Complex Systems; Joshi N; Australian Research Council (ARC)/Discovery Projects (DP).
 Mathematical biosciences network; Joshi N; Australian Research Council (ARC)/Special Research Initiatives.
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

Discrete Systems and Integrability (Cambridge University Press, 2016)















































