New Fellows Seminar
Wednesday, 7 May 2008

Hunting non-linear mathematical butterflies
by Professor Nalini Joshi

Nalini Joshi has a science degree from the University of Sydney and holds a PhD and MA from Princeton University in applied mathematics. She has held lecturing positions and fellowships at the Australian National University, the University of New South Wales, 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 the University of Cambridge. 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. Her research focuses on longstanding problems concerning the asymptotic and analytic structure of solutions to non-linear integrable equations. She has solved open problems for the classical Painlevé equations (differential equations that are archetypical non-linear models of modern physics) and discrete systems. Currently, she is obsessed with the analysis of cellular automata.

The utility of mathematical models relies on their ability to predict the future from a known set of initial states. But there are non-linear systems, like the weather, where future behaviours are unpredictable unless their initial state is known to infinite precision. This is the ‘butterfly effect’. I will show how to analyse functions to overcome this problem for the classical Painlevé equations, differential equations that provide archetypical non-linear models of modern physics.