I work in mathematical logic, computability theory and algorithmic randomness.

In algorithmic randomness we try to determine what it takes to produce randomness, and what you can do with it once you have it.

Logic and computability deal with the borders between the complete and the incomplete, the decidable and the undecidable, the computable and the non-computable. A fundamental result in the area is Gödel’s 1931 incompleteness theorem, which is a precise version of the following sentiment of Ishmail in Moby Dick.

I promise nothing complete; because any human thing supposed to be complete, must for that very reason infallibly be faulty.

Some open problems are available in a Banff research station archive file.