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William Boney

Assistant Professor
Faculty Profiles

Office: Elliott B211
Phone: 512.245.5254
Research Interest
Model Theory

I grew up in Austin, Texas and spent several lovely summers at Texas State University as part of the Mathworks program. I moved out of state to attend Grinnell College in Iowa. I got my Ph.D. at Carnegie Mellon University in Pittsburgh, PA in 2014. Prior to coming (back) to Texas State University, I had positions in Chicago and Boston.

My work is mostly in model theory, which is an area of logic. Rather than having anything to do with modeling, model theory is a kind of meta-mathematics that studies the way other people do mathematics and turns classes of structures (vector spaces, graphs, groups, etc.) into the objects of study. This allows model theory to both identify common causes of similar phenomena across mathematics and to transport techniques from one area to another.

I specifically work with nonelementary classes, those that require axioms beyond first-order logic to describe. Moving beyond first-order logic means that we lose the powerful compactness theorem, and much of my research is in finding what fragments of compactness can be recovered in different classes. This research naturally intersects with set theory, category theory, and different areas of algebra.

I enjoy math because I love working with friends and colleagues to solve interesting problems.