Sara Kališnik

My research focuses on applied algebraic topology (CV).

Papers by Topics:

• 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.
  • "Tropical Coordinates on the Space of Persistence Barcodes" in Foundations of Computational Mathematics.
  • "Symmetric Polynomials in Tropical Algebra Semirings" (joint work with Davorin Lesnik) in Journal of Symbolic Computation.
  • "Symmetric Polynomials in Upper-bound Semirings" (joint work with Davorin Lesnik) in Journal of Symbolic Computation.
  • "Tropical Sufficient Statistics for Persistent Homology" (joint work with Anthea Monod, Juan Angel Patino-Galindo, Lorin Crawford) In SIAM Journal on Applied Algebra and Geometry .
  • "Geometric and Probabilistic Limit Theorems in Topological Data Analysis" (joint work with Christian Lehn, Vlada Limic) submitted.
• 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.
  • "Finding the Homology of Manifolds using Ellipsoids" (joint work with Davorin Lesnik)(Supplementary programs are available here: AngleBetweenProjectionAndHalfline.nb, ProjectionNotOnHalfline.nb, ellipsoids.cpp).
• Parametrized Homology, Alexander Duality and Applications to Sensor Networks
  • "Parametrized Homology" (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.
• 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.