Peter Ulrickson's research interests include the use of algebraic and categorical tools in the treatment of problems arising in the consideration of abstract spaces, and in the connections of such with ideas arising in theoretical physics. Specifically, he has worked in relating spaces of quantum field theories to mathematical objects called cohomology theories, on algebra related to the study of knots. He is also studies notions of domination in graph theory, which is an abstraction of defending a general network of connected locations.
