I would like to sequence the genome of thermogenic plants to gain a better understanding of "autotrophic thermogenesis". Renewable heat is also interesting. (I wonder if I can keep 1000 gallons of water from freezing outside for a whole year?)
I heard Robert Lustig on Science Friday recently, and found his arguments about the damaging effects of sugar, particularly fructose, in the modern diet compelling.
After the Arab Spring, I wonder if any emerging democracies could build approval voting into their election systems. I really like this voting method.
I wonder if an optimal and efficient general algorithm exists that can solve all Travelling Salesperson Problems. (I think ant colony optimization algorithms and other swarm intelligence methods are promising.) I look for optimal solutions to common everyday problems all the time, so algorithms for solving TSPs remind me of the way my mind works!