Aaron Tyrrell

Postdoctoral Research Associate

Education

Ph.D. Mathematics, University of Notre Dame - 2021
M.Sc. Mathematics, Maynooth University, Maynooth, Co. Kildare, Ireland - 2016
B.Sc. Pure Mathematics, Maynooth University, Maynooth, Co. Kildare, Ireland - 2015

Research Group

Differential Geometry

Research Area

Geometric Analysis

Bio

Research Interests:

Conformal Geometry and Minimal Hypersurfaces

Selected Publications: 

• Matthew J. Gursky, Stephen E. McKeown and Aaron J. Tyrrell, Renormalized Volume of Minimally Bounded Regions in Asymptotically Hyperbolic Einstein Spaces, Advances in Theoretical and Mathematical Physics, Volume 26, 3081-3123 2022.

• Aaron J. Tyrrell, Renormalized Area for Minimal Hypersurfaces of 5D Poincaré-Einstein Spaces, Journal of Geometric Analysis 33, 310, 2023.

• Jeffrey S. Case and Aaron J. Tyrrell, A Sharp Inequality for Trace-Free Matrices with Applications to Hypersurfaces, Proceedings of the AMS, 152, 823-828, 2024.

• Jeffrey S. Case, C. Robin Graham, Tzu-Mo Kuo, Aaron J. Tyrrell and Andrew Waldron, A Gauss-Bonnet Formula for the Renormalized Area of Minimal Submanifolds of Poincaré-Einstein Spaces, Communications in Mathematical Physics 53, 406, 2025.