Adam Martens

About

I'm a Ph.D. candidate at UBC under the supervision of Albert Chau. I have had my entire post-secondary education from UBC, wherein I have obtained BSc (2019) and MSc (2021).

My current research is primarily focused on Hamilton's Ricci Flow, though I remain interested in other aspects of geometric analysis as well as mathematical general relativity.

The differential geometry group at UBC organizes a weakly learning seminar. For more information on how to participate, as well as upcoming schedule and past recordings, see here.

A somewhat up-to-date photo of my daughters (they're extraordinarily cute!).

Teaching

I always welcome correspondence from past, present or future students. You may be interested in my teaching philosophy, or in a list of courses for which I have been a TA.

Papers

• Removing scalar curvature assumption for Ricci flow smoothing arXiv


• Sharpening a gap theorem: nonnegative Ricci and small curvature concentration. arXiv


• Long-time Ricci flow existence and topological rigidity from manifolds with pinched scale-invariant integral curvature (with Albert Chau). arXiv


• Pseudolocality and completeness for nonnegative Ricci curvature limits of 3D singular Ricci flows (with Albert Chau). Math. Z. 307 (2024), no. 4, Paper No. 63. arXiv


• Bartnik mass of non-negatively curved CMC spheres and Degenerate Apparent Horizons (with Albert Chau). To appear in Proceedings of the American Mathematical Society. (2022) arXiv


• Goormaghtigh's Equation : Small Paramaters (with Michael Bennett and Ben Garbuz). Publ. Math. Debrecen 96 (2020), no. 1-2, 91-110.