Mathematical problems in fusion research

For half a century, nuclear fusion has been a dream of humanity: clean, inexhaustible energy without the problems of fossil fuels, nuclear fission or conventional renewable energy sources. In this talk, I shall give a general introduction into fusion research, describe its current status (including the new Wendelstein 7-X experiment in Greifswald), but the emphasis of the talk will be on mathematics. In particular, I will describe a few concrete, unsolved mathematical problems whose solution would be greatly appreciated.