Research

Magnitude of metric spaces

• "Alpha magnitude" (joint work with Miguel O'Malley and Nina Otter). In Journal of Pure and Applied Algebra, Volume 227(11), 107396, 2023.

Tropical Semirings and Applications in TDA

• "Symmetric and r-Symmetric Tropical Polynomials and Rational Functions" (joint work with Gunnar Carlsson). In Journal of Pure and Applied Algebra, Volume 220(11), pages 3610–3627, 2016.
• "Tropical Coordinates on the Space of Persistence Barcodes" in Foundations of Computational Mathematics, Volume 19, pages 101–129, 2019.
• "Symmetric Polynomials in Tropical Algebra Semirings" (joint work with Davorin Lesnik). in Journal of Symbolic Computation, Volume 93, pages 100–119, 2019.
• "Symmetric Polynomials in Upper-bound Semirings" (joint work with Davorin Lesnik). in Journal of Symbolic Computation, Volume 103, pages 280–299, 2021.
• "Tropical Sufficient Statistics for Persistent Homology" (joint work with Anthea Monod, Juan Angel Patino-Galindo and Lorin Crawford). In SIAM Journal on Applied Algebra and Geometry , Volume 3, Issue 2, 2019.
• "Geometric and Probabilistic Limit Theorems in Topological Data Analysis" (joint work with Christian Lehn and Vlada Limic). In Advances in Applied Mathematics, Volume 131, 102244.

Connecting Algebraic Geometry and Applied Topology

The main reason for doing a postdoc at the Max-Planck Institute was to learn more algebraic geometry and to deepen the connections between the applied topology and applied algebraic geometry communities. The following paper is the first result in that direction.

• "Learning Algebraic Varieties from Samples" (joint work with Bernd Sturmfels, Paul Breiding and Madeleine Weinstein). In Revista Matemática Complutense, Volume 31, pages 545–593, 2018.
• "Finding the Homology of Manifolds using Ellipsoids" (joint work with Davorin Lesnik). Supplementary programs are available here: AngleBetweenProjectionAndHalfline.nb, ProjectionNotOnHalfline.nb, ellipsoids.cpp. Accepted for publication in Journal of Applied and Computational Topology.

Parametrized Homology, Alexander Duality and Applications to Sensor Networks

• "Parametrized Homology via zigzag persistence" (joint work with Gunnar Carlsson, Vin de Silva and Dmitriy Morozov). In Algebraic and Geometric Topology.
• "Alexander Duality for Parametrized Homology". In Homology, Homotopy and Applications, Volume 15(2), pages 227–243.

Skeletonization Problem

• "The Higher-Dimensional Skeletonization Problem" (joint work with Vitaliy Kurlin and Davorin Lesnik). In Advances in Applied Mathematics, Volume 102, pages 113–142, 2019.

Shape of Molecules

• "Extended topological persistence and contact arrangements in folded linear molecules" (joint work with Alireza Mashaghi). In Frontiers in Applied Mathematics and Statistics, Mathematics of Molecules, 2016, Volume 2, 2016.