David Brander

Integrable systems in geometry is an area of mathematics that studies special geometries associated to so-called integrable nonlinear partial differential equations. These are special equations that are important in physics and, despite being nonlinear, can often be solved using ideas that come from a spectrum of mathematical disciplines. Most of the integrable systems that are studied are harmonic maps from surfaces into higher dimensional spaces, and these are fundamental, being a special case of the famous Yang-Mills equations. I have been interested in integrable systems since my PhD work at Australian National University (ANU) in Canberra in 2002-2005, and I started collaborations with researchers in Japan during a JSPS postdoctoral position in 2006-2008 at Kobe University. After moving to Denmark in 2008, I maintained some interactions with Japanese collaborators. In my research field there is quite a strong Japanese involvement; so connections, either through collaborations or simply meeting at conferences, is helpful. To facilitate this, in 2018 I applied for a JSPS Bridge Fellowship to visit Professor Shimpei Kobayashi at Hokkaido University. My goals were a) to get started on a research project with Professor Kobayashi that we had already discussed at a meeting in Germany, and b) to give some research presentations about my research and explore other possible future collaborations.

The research visit was 19 days in October, which, though cool in Sapporo, is still a nice time to visit. Hokkaido University has a beautiful campus, which is even a tourist attraction visited by a noticeable number of Japanese and Chinese tourists. The many large trees were green when I arrived, but already red and yellow by the end of my visit. Professor Kobayashi arranged two workshops while I was there; one on integrable geometry, and another on geometry and design, which is another of my research interests. These were small workshops where we could actually have deep research discussions – the kind of workshop that usually turns out to be the most useful and productive. I met researchers from Tsukuba, Kobe, Kyushu and Shizuoka Universies. During my stay, I also visited Kyushu University to attend a workshop and give a research presentation there.

As for my previous trips to Japan, the visit was very pleasant and stress-free, and the food was great. From a research perspective I think the goals were achieved: I have started at least two new research collaborations involving three researchers from Japan and one from China, and made new connections there that I will meet again later this year at another conference. One of the research projects is also an introduction for me to a new and interesting research topic from mathematical physics. So I am very happy with the outcome of this fellowship. I would like to thank JSPS for their support allowing me to once again visit this unique country. I hope to go again soon.