My name is Aaron Tyrrell and I am a Postdoctoral Research Associate at the University of Notre Dame. Before this I was a Lecturer & Researcher at Texas Tech University, and I spent a year as a Research Associate at the University of Texas at Dallas; working with Professor Stephen McKeown. I finished my Ph.D. in 2021 at the University of Notre Dame under the supervision of Professor Matthew Gursky. My thesis was titled Renormalized Volume and Area. I began my current position at Notre Dame in August 2025.

My research interests lie primarily in an area of geometric analysis that is connected to the holographic study of conformal geometry initiated by Fefferman and Graham. In particular, I focus on questions around renormalized area and volume and their connections to other areas of geometry such as generalized Willmore energies and the theory of minimal submanifolds in hyperbolic space. Recently I have worked on problems related to the first eigenvalue of the Laplace operator on asymptotically hyperbolic manifolds and their submanifolds. I am also interested in the theory of hypersurfaces in space forms and general Einstein manifolds.

My pre-prints and publications are available here: Papers. I recently attended the International Doctoral Summer School in Conformal Geometry and Non-Local Operators at IMAG at Universidad de Granada:

I am also passionate about teaching. I was recently honored to receive the Professing Excellence award after my first semester teaching at Texas Tech:

Professing Excellence

I believe in carefully planned lectures that present material in a way that includes the students in a process of discovery. I want the students to feel confident that they can see how one might come up with these ideas. I believe in “practice makes perfect” along with patience, encouragement, and a positive attitude. I also make an effort to be approachable and friendly towards my students. This allows me to get ahead of any issues that the students might be having and creates an environment conducive to learning.