Hill Researching “Mysterious” Zero-One Laws in Mathematics Department

Cameron Donnay Hill, assistant professor of mathematics, joined the faculty this fall.

Cameron Donnay Hill is an assistant professor of mathematics.

In this Q&A we speak with Cameron Donnay Hill, assistant professor of mathematics. Hill joined the Wesleyan faculty this fall.

Q: Professor Hill, welcome to Wesleyan! What attracted you to the University and the Department of Mathematics and Computer Science?

A: Wesleyan provides a wonderful balance between teaching and research that can be found almost nowhere else, and I can only think of a few additional places where the “average” undergrad is remarkably clever and curious.

Q: What are your research interests?

A: I’m mostly interested in questions about “finite and discrete” mathematical objects, but my research program is to adapt technology originally developed for “infinite and smooth(ish)” objects for studying my finite, discrete things. Right now, I’m specifically studying two phenomena known as zero-one laws and Ramsey properties, respectively.

Q: Please explain what a zero-one law is.

A: If you have a collection of objects and some property, one can sometimes say “all but a negligible fraction of the objects in my collection have this property.” Really, we are interested in collections of properties, too, so the zero-one law will say something like, “for each of these properties, all but a negligible fraction of the *large enough* objects in my collection have that property.” Up to now, when I’ve said “collection of objects,” I’ve been talking about finite things, but when this zero-one law phenomenon happens, we find ourselves with an infinite object that has all of those properties and just generally represents the collection of finite objects but is far, far easier to work with.

Q: Will you continue this research at Wesleyan, or what do you hope to ultimately accomplish?

A: Unless something much more interesting comes along (which I doubt), I will keep going along the same research program. In the near term, I and several other logicians in New England hope to get a hold of zero-one laws in particular, which on the whole are quite mysterious to humans right now.

Q: What classes are you teaching this year?

A: This fall, I am teaching one calculus class and a set theory course for math majors. In the spring, I’ll actually be away at a semester-long research workshop in Berkeley, Calif. along with Professor Philip Scowcroft and Professor Carol Wood.

Q: Have you authored any papers? If so, please list any recent publications.

A: Yes. Recently I’ve had papers published in The Annals of Pure and Applied Logic and Algorithmica. My paper on “Well-quasi-orders, quasi-finite axiomatizability and AZ-enumerability” will appear in the Journal of Symbolic Logic, and another, titled “Local dp-rank and vc-density over indiscernible sequences” will appear in Mathematical Logic Quarterly. You can see all my publications on my website.

Q: Where are you from, and where did you complete your undergraduate and graduate studies? Where were you working prior to Wesleyan?

A: I’m originally from Los Angeles, Calif. I went to college at Yale University where I got a BA in Russian and East European studies. After some puttering around, I went to graduate school in Mathematics at UC Berkeley, graduating in 2010. Since then, I was postdoc at the University of Notre Dame until I came here to Wesleyan.

Q: Aside from zero-one laws, what are your interests?

A: In principle, I like to draw and paint, and I have half-way written some science fiction stories. Over the past three years, I haven’t really allowed myself much free time, so it will be nice to try my hand at those things again.