# 26th Annual Charles R. DePrima Memorial Lecture in Mathematics

## Dr. Nalini Joshi

Professor of Mathematics

University of Sydney

### Thursday, October 13, 2016

4:00 PM 151 Sloan

"Symmetry Through Geometry"

The search for symmetries of differential equations set in motion the development of extraordinarily important areas of mathematics. In this talk, we provide a new perspective on the corresponding problem for difference equations, by using a simple, beautiful geometric structure revealed in our recent study. The objects of this study are partial difference equations that arise as discrete versions of this study are partial difference equations that arise as discrete versions of famous PDEs, like the Korteweg-de Vries equation. These discrete systems consist of equations fitted together in a self-consistent way on a square, a 3-cube or an N-dimensional cube. By using the beautiful geometric structure of space-filling polytopes, we show how to find their unexpected symmetry reductions.

This lecture will be accessible to a general audience

Nalini Joshi is an Australian mathematician, and Australian Laureate Fellow and Professor in the school of Mathematics and Statistics at the University of Sydney. She gained her BSc at the University of Sydney and her Ph.D at Princeton University. In 2002, she moved to the University of Sydney as Chair of Applied Mathematics; since 2006 she has been director of the Centre for Mathematical Biology, from 2007 to 2009 head of the School of Mathematics and Statistics. Joshi was elected Fellow of the Australian Academy of Science in March 2008 and has held a number of positions in the Australian Mathematical Society, including its presidency from December 2008 to September 2010. In 2012, she received the Georgina Sweet Fellowship for women in science and technology disciplines. In 2015, she was the 150th Anniversary hardy Lecturer, an award by the London Mathematical Society.