Ph.D. Candidate

Department of Mathematics

University of British Columbia

1984 Mathematics Road

Vancouver, B.C.

Canada V6T 1Z2

Office: | MATH 124 |

E-mail: | martens@math.ubc.ca |

I'm a Ph.D. candidate at UBC under the supervision of Professor 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!).

I always welcome correspondence from past, present or future students. Here is a list of courses for which I have been a TA.

2024 | Fall: | MATH 100 (Differential Calculus) Section 1B2 |

2024 | Spring: | MATH 101 (Integral Calculus) Sections C17, C22, C32 |

2023 | Fall: | MATH 100 (Differential Calculus) Sections A16, A23, A33, A48 |

2021 | Fall: | MATH 102 (Differential Calculus with Applications to Life Sciences) Section 105 |

- 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.