Computational Topology Link to heading

Steinhaus Filtration and Stable Paths in the Mapper, Symposium on Computational Geometry, 2025.

Abstract: We define a new filtration called the Steinhaus filtration built from a single cover based on a generalized Steinhaus distance, a generalization of Jaccard distance. The homology persistence module of a Steinhaus filtration with infinitely many cover elements may not be $q$-tame, even when the covers are in a totally bounded space. While this may pose a challenge to derive stability results, we show that the Steinhaus filtration is stable when the cover is finite.

Matrix Theory Link to heading

Realizing Suleĭmanova spectra via permutative matrices, II, Linear Algebra and its Applications, Volume 566, 2019, Pages 183-198.

Abstract: In this work, the real nonnegative inverse eigenvalue problem is solved for a particular class of permutative matrix. The necessary and sufficient condition there is also shown to be sufficient for the symmetric nonnegative inverse eigenvalue problem.

On the realizability of the critical points of a realizable list, Linear Algebra and its Applications, Volume 555, 2018, Pages 301-313.

Abstract: The nonnegative inverse eigenvalue problem (NIEP) is to characterize the spectra of entrywise nonnegative matrices. Johnson conjectured that the list of critical points must be realizable. In this work, Johnson’s conjecture, and consequently Monov’s conjecture, is established for a variety of important cases including Ciarlet spectra, Suleĭmanova spectra, spectra realizable via companion matrices, and spectra realizable via similarity by a complex Hadamard matrix.

Presentations Link to heading

• CG Week 2025, Kanazawa, JPN. June 23-27, 2025.
• Undergraduate Poster Session at the Joint Mathematics Meetings, San Diego, CA. January 12, 2018.
• University of Washington Undergraduate Research Symposium, Seattle, WA. May 18, 2017.