Tag Archive for Cameron Hill

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.