Small scale fusion power.
Research challenges: How to get hydrogen to fuse into helium using only 500kg of machinery and less energy than will be produced.
Urgent Tasks: (In-)Validate the results of the fusor people, scale up / down as neccessary.
Reasons: Enormous amounts of energy goes into everything. If energy costs drop significantly, I expect sustained, fast and profound economic growth, in this case without too much ecological impact. Also, a lot of high-energy technology will become way more feasible, e.g. space missions.
I have just received a survey questionnaire regarding future directions in EU (European Union) research funding, and thought it would be interesting to see how LessWrong would answer the main question:
Imagine that EU funding is available for one ambitious, visionary project extending beyond 2020.