I am thinking about the design of quantum money, quantum copy-protected programs, and quantum program obfuscation. Basically, understanding whether and how quantum computers can implement the strongest possible cryptographic operations (all of which are known to be classically impossible and to have a wide range of applications).

I am working on the development of collaborative filtering / recommendation protocols for large communities. This includes, for example, a system for aggregating product reviews which is robust to the presence of large numbers of planted reviews, or a system for spam filtering based on trust which remains robust in the presence of a supermajority of sophisticated spammers. More generally, this work seems like an important first step in the development of automated and robust systems of trust.

I started working on these projects because they were interesting problems I was well equipped to work on which seemed likely to yield publications in time for graduate school applications (optimistically, these positions have been born out in both cases). I don't recommend this decision making process.

I think automating trust and designing better recommendation systems are more important than the overwhelming majority of theoretical problems currently studied, but I have realized more recently that there are more important issues to deal with. I am continuing to work on these problems now because of inertia, the fallacy of sunk costs, and a desire for status.