Assistant Professor of Mathematics and Computer Information Systems
Areas of Expertise: Mathematical logic
My parents gave me an Atari 400 when I was very young, and it came with a BASIC interpreter. I somehow got a book that showed how to program short games that would do things like move an “@” symbol around in a field of “*” symbols. I found this deeply impressive. Later, in college, I read a book called Excursions in Number Theory, by C. Stanley Ogilvy, which made me reconsider mathematics. As a philosophy major, I had absorbed a Spinozistic reverence for all things mathematical, and when I realized I was relatively good at it, I decided to make it a career.
Mathematical logic has a lot to do with the definability of concepts in formal languages. So does AI, and I have always been attracted to the confluence between those two things – the interplay of the nature of a concept and how its complexity is reflected in its possible representations.
My official research is in what are called NIP theories, which is a subspecialization within model theoretic stability theory. This can be rephrased, without too much loss, as the study of relations with finite VC dimension. When I was just beginning my PhD research, there had been breakthroughs in applying some abstract model theory to practical questions relating to Artificial Neural Networks. For a long time, I tried to improve these results, but ended up doing the opposite of what I meant to do. Namely, I imported an idea from machine learning into model theory, which has proven to be fruitful. Since then, my work has been more model theoretic, but I am always looking for opportunities to go back in a CS direction.