Thursday, November 19, 2020

Vaughan Jones and Kaikoura

Vaughan Jones, one of the greatest mathematicians from New Zealand, passed away on September 6 at 67. Jones is an expert in knot theory among other areas and received the Fields Medal in 1990.

The Jones polynomial captures information about knots. Vaughan Jones himself co-authored a paper on a polynomial-time quantum algorithm for approximating the Jones polynomial, one of the few natural problems outside of factoring that has an exponential improvement with a quantum algorithm. 

From his Vanderbilt obituary

One way he worked to improve the field of mathematics in his native country was to organize a “summer school” in January each year and attract leading mathematicians from around the world to give lectures and interact with local students and professional mathematicians at a variety of beautiful locations around New Zealand. Out of this activity grew the New Zealand Mathematics Research Institute, which he co-founded and then led from the mid-1990s to this year.

I had the pleasure of teaching in one of those summer schools in January 2000 in Kaikoura on the South Island. In between the whale watching, mountain hiking, jogging, gorging on mussels, and Maori ceremonies, the NZMRI summer school Aspects of Complexity had short courses to a mix of students and researchers in complexity and logic. I gave some lectures on Kolmogorov complexity that preceded a study of algorithmic randomness in the logic community. Other speakers included Eric Allender on basic complexity, Felipe Cucker on real computation, Mike Fellows on parameterized complexity, and Dominic Welsh on counting complexity. 

It took me 36 hours door-to-door to get to Kaikoura but definitely worth it. Thanks to Vaughan Jones, for his research, his polynomial and creating a summer school that gave me that one perfect week in New Zealand.

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