Research
Focus Areas: Theory, Computational Logic, Type Theory, Complexity Theory, Randomness
My interest in the computational properties of random and generic sets goes back to my thesis, written under the supervision of Carl Jockusch in Mathematics at the University of Illinois. Unlike most people working in computational complexity theory, my understanding of randomness is based on measure theory and definability rather than compressibility.
Another long-term research interest is the Berman-Hartmanis Isomorphism Conjecture, which holds that all NP-complete sets are isomorphic under polynomial-time computable and invertable 1-1 reductions. Just for the record, I believe that the conjecture is false.
I’m currently coming up to speed on type theory, approaching it as a mash-up of formal logic and functional programming.
