Research interests & current projects
My interest in and knowledge of differential geometry and its discretizations comes primarily from my PhD research. During my stay at the TU Berlin I also worked a lot with spaces of constant curvature, and out of those mainly with the hyperbolic space.
I apply differential geometry to analyze algebraic objects called amoebas. This is a joint project with Timo de Wolff.
I use spaces of constant curvature to investigate triangulations and homotopy reconstruction on higher-dimensional Riemannian manifolds. These are joint projects with, among others, Dominique Attali, André Lieutier, and Mathijs Wintraecken.
I also use spaces of constant curvature to gain insight into the theory of Bregman divergences, with the goal of extending persistent homology to work with this class of distance measures. This is a joint project with Herbert Edelsbrunner and Hubert Wagner.
Publications & preprints
Published and accepted articles
H.Dal Poz Kouřimská, A. Lieutier, and M. Wintraecken. The medial axis of closed bounded sets is Lipschitz stable with respect to the Hausdorff distance under ambient diffeomorphisms. 40th International Symposium on Computational Geometry (2024). Available on ArXiv
D. Attali, H.Dal Poz Kouřimská, C. Fillmore, I. Ghosh, A. Lieutier, E. Stephenson, and M. Wintraecken. Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds. 40th International Symposium on Computational Geometry (2024). Available on ArXiv
D. Attali, H.Dal Poz Kouřimská, C. Fillmore, I. Ghosh, A. Lieutier, E. Stephenson, and M. Wintraecken. The ultimate frontier: An Optimality Construction for Homotopy Inference. Computational Geometry Media Exposition, CG Week 2024. Video available on YouTube
H. Dal Poz Kouřimská. Discrete Yamabe problem for polyhedral surfaces. Discrete Comput Geom 70, 123–153 (2023). https://doi.org/10.1007/s00454-023-00484-2
H. Kouřimská, L. Skuppin, and B. Springborn. A variational principle for cyclic polygons with prescribed edge lengths. In: Bobenko, A. (eds) Advances in Discrete Differential Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-50447-5_5
Published in workshop proceedings
H. Dal Poz Kouřimská and M. Wintraecken. Stability of circumcentres for small metric perturbations of spaces of constant curvature. CG:YRF 2022. See the YRF booklet, page 109
H.Dal Poz Kouřimská and M. Wintraecken. Curvature variation based adaptive sampling for Delaunay triangulations of Riemannian manifolds. EuroCG2022 . See the EuroCG booklet, Contributed paper nr. 23
Science communication & outreach articles
H. Dal Poz Kouřimská and M. Thalhammer. Report on the fourth Austrian Day of Women in Mathematics, International Mathematical News, August 2024, Issue Nr. 255, June 2024 (to appear). https://www.oemg.ac.at/2024/06/13/imn-255.html
H. Dal Poz Kouřimská and M. Thalhammer. Report on the third Austrian Day of Women in Mathematics, International Mathematical News, August 2023, Issue Nr. 253, August 2023. www.oemg.ac.at/IMN/imn253.pdf
L. Boßmann, H. Dal Poz Kouřimská, and M. Thalhammer. Report on the Austrian Day of Women in Mathematics and further A2WiM activities 2022, International Mathematical News, Issue Nr. 250, August 2022. www.oemg.ac.at/IMN/imn250.pdf
H. Adams, H. Dal Poz Kouřimská, T. Heiss, S. Percival, and L. Ziegelmeier. How to tutorial-a-thon. Notices of the American Mathematical Society 2021;68(9):1511-1514. doi:10.1090/noti2349
H. Dal Poz Kouřimská, E. Dragoti-Cela, A. Molchanova, and M. Thalhammer. Report on the First Austrian Day of Women in Mathematics. International Mathematical News, Issue Nr. 247, August 2021. www.oemg.ac.at/IMN/imn247.pdf
PhD thesis
Kouřimská, Hana. Polyhedral surfaces of constant curvature and discrete uniformization. May 2020. dx.doi.org/10.14279/depositonce-9883
Recordings of my talks
Tight bounds for learning homotopy, Computational Persistence workshop, September 29, 2023
Curvature variation based sampling for Delaunay triangulations of manifolds, AATRN seminar, April 20, 2022
Uniformization with a new discrete Gaussian curvature, FRG Workshop on Geometric Methods for Analyzing Discrete Shapes, May 7, 2021