[{"keyword":["Triangulation of manifolds","Simplicial approximation","CW complexes","Delaunay complexes","List homomorphism problem","Topological Data Analysis"],"corr_author":"1","department":[{"_id":"UlWa"}],"has_accepted_license":"1","article_processing_charge":"Yes","publication_identifier":{"eissn":["1868-8969"],"isbn":["9783959774185"]},"abstract":[{"text":"Simplicial approximation provides a framework for constructing simplicial complexes that are homotopy equivalent to a given manifold, provided a CW structure is explicitly known. However, its conventional implementation quickly becomes intractable on a computer: barycentric subdivision produces poorly shaped simplices, and the star condition introduces many vertices. To address these limitations, this article develops a subdivision scheme based on spherical Delaunay triangulations, which attains better refinement properties than barycentric subdivisions. Moreover, the star condition is reframed as two independent problems, one geometric and the other combinatorial, respectively tackled in the language of locally equiconnected spaces and the list homomorphism problem, allowing an exponential reduction in the number of vertices. Via a prototype implementation, we obtain simplicial complexes homotopy equivalent to Grassmannians and Stiefel manifolds up to dimension 5.","lang":"eng"}],"citation":{"short":"R. Tinarrage, in:, 42nd International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026.","chicago":"Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations.” In <i>42nd International Symposium on Computational Geometry</i>, Vol. 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">https://doi.org/10.4230/LIPIcs.SoCG.2026.93</a>.","ama":"Tinarrage R. Simplicial approximation to CW complexes with spherical Delaunay triangulations. In: <i>42nd International Symposium on Computational Geometry</i>. Vol 367. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2026. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">10.4230/LIPIcs.SoCG.2026.93</a>","ieee":"R. Tinarrage, “Simplicial approximation to CW complexes with spherical Delaunay triangulations,” in <i>42nd International Symposium on Computational Geometry</i>, New Brunswick, NJ, United States, 2026, vol. 367.","ista":"Tinarrage R. 2026. Simplicial approximation to CW complexes with spherical Delaunay triangulations. 42nd International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry vol. 367, 93:1-93:22.","mla":"Tinarrage, Raphaël. “Simplicial Approximation to CW Complexes with Spherical Delaunay Triangulations.” <i>42nd International Symposium on Computational Geometry</i>, vol. 367, 93:1-93:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">10.4230/LIPIcs.SoCG.2026.93</a>.","apa":"Tinarrage, R. (2026). Simplicial approximation to CW complexes with spherical Delaunay triangulations. In <i>42nd International Symposium on Computational Geometry</i> (Vol. 367). New Brunswick, NJ, United States: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2026.93\">https://doi.org/10.4230/LIPIcs.SoCG.2026.93</a>"},"file_date_updated":"2026-06-22T07:53:13Z","doi":"10.4230/LIPIcs.SoCG.2026.93","title":"Simplicial approximation to CW complexes with spherical Delaunay triangulations","date_updated":"2026-06-22T11:28:26Z","ddc":["500"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","_id":"22000","external_id":{"arxiv":["2112.07573"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"month":"05","scopus_import":"1","oa_version":"Published Version","article_number":"93:1-93:22","conference":{"end_date":"2026-06-05","name":"SoCG: Symposium on Computational Geometry","start_date":"2026-06-02","location":"New Brunswick, NJ, United States"},"fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2026.93","arxiv":1,"publication_status":"published","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication":"42nd International Symposium on Computational Geometry","date_created":"2026-06-14T22:01:43Z","date_published":"2026-05-27T00:00:00Z","oa":1,"researchdata_availability":"no","status":"public","year":"2026","intvolume":"       367","related_material":{"link":[{"relation":"software","url":"https://doi.org/10.5281/zenodo.19251455"}]},"type":"conference","author":[{"orcid":"0000-0002-1404-1095","id":"40ebcc9d-905f-11ef-bf0a-dc475da8a04e","last_name":"Tinarrage","first_name":"Raphaël","full_name":"Tinarrage, Raphaël"}],"day":"27","OA_place":"publisher","das_tickbox":"0","supplementarymaterial":"yes","volume":367,"OA_type":"gold","file":[{"content_type":"application/pdf","file_id":"22111","success":1,"file_size":1436035,"creator":"dernst","date_created":"2026-06-22T07:53:13Z","access_level":"open_access","file_name":"2026_LIPIcSSoCG_Tinarrage.pdf","date_updated":"2026-06-22T07:53:13Z","relation":"main_file","checksum":"a468edad327962309688aa78678138da"}],"quality_controlled":"1"},{"volume":8,"OA_type":"green","article_type":"original","quality_controlled":"1","author":[{"first_name":"Sebastiano","full_name":"Cultrera di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano"},{"full_name":"Draganov, Ondrej","first_name":"Ondrej","last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0464-3823"},{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"day":"01","OA_place":"repository","ec_funded":1,"page":"30-62","date_created":"2025-11-02T23:01:33Z","date_published":"2026-03-01T00:00:00Z","oa":1,"year":"2026","status":"public","related_material":{"record":[{"relation":"earlier_version","id":"15091","status":"public"}]},"mathsc":["62R40","55N31","68T09","57Q70"],"intvolume":"         8","type":"journal_article","fulldoi":"https://doi.org/10.3934/fods.2025003","publication_status":"published","arxiv":1,"publication":"Foundations of Data Science","project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","grant_number":"I02979-N35"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"month":"03","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.03128"}],"oa_version":"Preprint","title":"Chromatic alpha complexes","date_updated":"2026-10-02T11:56:12Z","ddc":["510"],"_id":"20585","publisher":"AIMS","external_id":{"arxiv":["2212.03128"]},"acknowledgement":"This project has received funding from the European Research\r\nCouncil (ERC) under the European Union’s Horizon 2020 research and innovation\r\nprogramme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund\r\n(FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR\r\n109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.","keyword":["Topological data analysis","Delaunay mosaic","alpha complex","chromatic sets","persistent homology","kernel/image/cokernel persistent homology","radius function","discrete Morse theory","exact sequences"],"corr_author":"1","department":[{"_id":"HeEd"}],"has_accepted_license":"1","article_processing_charge":"No","publication_identifier":{"eissn":["2639-8001"]},"abstract":[{"lang":"eng","text":"Motivated by applications in medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, kernels and cokernels, we design provably stable homological quantifiers that describe the geometric micro- and macro-structure of how the color classes mingle. These can be efficiently computed using chromatic variants of Delaunay and alpha complexes, and code that does these computations is provided."}],"doi":"10.3934/fods.2025003","citation":{"mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>, vol. 8, AIMS, 2026, pp. 30–62, doi:<a href=\"https://doi.org/10.3934/fods.2025003\">10.3934/fods.2025003</a>.","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2026). Chromatic alpha complexes. <i>Foundations of Data Science</i>. AIMS. <a href=\"https://doi.org/10.3934/fods.2025003\">https://doi.org/10.3934/fods.2025003</a>","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” <i>Foundations of Data Science</i>, vol. 8. AIMS, pp. 30–62, 2026.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2026. Chromatic alpha complexes. Foundations of Data Science. 8, 30–62.","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Foundations of Data Science 8 (2026) 30–62.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” <i>Foundations of Data Science</i>. AIMS, 2026. <a href=\"https://doi.org/10.3934/fods.2025003\">https://doi.org/10.3934/fods.2025003</a>.","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. <i>Foundations of Data Science</i>. 2026;8:30-62. doi:<a href=\"https://doi.org/10.3934/fods.2025003\">10.3934/fods.2025003</a>"}},{"status":"public","year":"2025","related_material":{"record":[{"relation":"part_of_dissertation","id":"15091","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"18981"}]},"type":"dissertation","date_created":"2025-01-31T17:04:40Z","date_published":"2025-02-03T00:00:00Z","oa":1,"fulldoi":"https://doi.org/10.15479/at:ista:18979","publication_status":"published","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"file_size":11899491,"creator":"odragano","content_type":"application/zip","file_id":"18983","checksum":"af6567e5d35e5eb330b8925ae37f1998","relation":"source_file","date_updated":"2025-01-31T16:58:30Z","access_level":"closed","date_created":"2025-01-31T16:58:30Z","file_name":"Thesis.zip"},{"checksum":"c3fef68e35b9dc2020b2ca6006da6343","date_updated":"2025-02-04T16:22:07Z","relation":"main_file","access_level":"open_access","date_created":"2025-02-04T16:22:07Z","file_name":"Thesis.pdf","file_size":8857514,"creator":"odragano","file_id":"19000","content_type":"application/pdf"}],"supervisor":[{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833"}],"OA_place":"publisher","page":"140","author":[{"orcid":"0000-0003-0464-3823","last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","first_name":"Ondrej","full_name":"Draganov, Ondrej"}],"day":"03","ddc":["514","004"],"date_updated":"2026-10-02T11:57:00Z","_id":"18979","publisher":"Institute of Science and Technology Austria","degree_awarded":"PhD","acknowledgement":"The research presented in this thesis was funded with the Wittgenstein Prize,\r\nAustrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.\r\n","title":"Structures and computations in topological data analysis","article_processing_charge":"No","abstract":[{"lang":"eng","text":"Topological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA.\r\n\r\nThe first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue.\r\n\r\nThe aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor.\r\n\r\nWe describe a construction of a chromatic alpha complex, which enables  efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline.\r\n\r\nThe second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory.\r\n\r\nIn the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot."}],"publication_identifier":{"issn":["2663-337X"]},"doi":"10.15479/at:ista:18979","citation":{"ista":"Draganov O. 2025. Structures and computations in topological data analysis. Institute of Science and Technology Austria.","ieee":"O. Draganov, “Structures and computations in topological data analysis,” Institute of Science and Technology Austria, 2025.","ama":"Draganov O. Structures and computations in topological data analysis. 2025. doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>","chicago":"Draganov, Ondrej. “Structures and Computations in Topological Data Analysis.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>.","short":"O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.","apa":"Draganov, O. (2025). <i>Structures and computations in topological data analysis</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>","mla":"Draganov, Ondrej. <i>Structures and Computations in Topological Data Analysis</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>."},"file_date_updated":"2025-02-04T16:22:07Z","keyword":["topological data analysis","chromatic point set","alpha complex","persistent homology","six pack","sheaf","microlocal discrete Morse","injective resolution","collapse","knot","discrete Morse theory"],"alternative_title":["ISTA Thesis"],"corr_author":"1","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"has_accepted_license":"1","project":[{"grant_number":"I02979-N35","call_identifier":"FWF","name":"Persistence and stability of geometric complexes","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"Z00342"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"month":"02","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd"},{"doi_confirm":"1","author":[{"first_name":"Teresa","full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","orcid":"0000-0002-1780-2689"}],"day":"17","OA_place":"publisher","ec_funded":1,"page":"111","das_tickbox":"0","supplementarymaterial":"no","supervisor":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert"}],"file":[{"success":1,"content_type":"application/pdf","file_id":"18686","creator":"theiss","file_size":7752253,"file_name":"Teresa_Heiss_PhD_Thesis_final.pdf","access_level":"open_access","date_created":"2024-12-19T10:24:46Z","checksum":"247bb057aed2fba1cd4711917aaa2d77","date_updated":"2024-12-19T10:24:46Z","relation":"main_file"},{"checksum":"9648b45c07a008ee11a07f99856a139d","date_updated":"2024-12-19T10:24:50Z","relation":"source_file","access_level":"closed","date_created":"2024-12-19T10:24:50Z","file_name":"PhD_Thesis.zip","file_size":17197731,"creator":"theiss","content_type":"application/zip","file_id":"18687"}],"fulldoi":"https://doi.org/10.15479/at:ista:18667","publication_status":"published","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_created":"2024-12-17T16:17:55Z","date_published":"2024-12-17T00:00:00Z","oa":1,"year":"2024","status":"public","researchdata_availability":"no","related_material":{"record":[{"status":"public","id":"10828","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"11440"},{"relation":"part_of_dissertation","status":"public","id":"9345"},{"status":"public","id":"18673","relation":"part_of_dissertation"}]},"type":"dissertation","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"month":"12","oa_version":"Published Version","project":[{"grant_number":"788183","call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"}],"keyword":["persistent homology","topological data analysis","periodic","crystalline materials","images","fingerprint"],"alternative_title":["ISTA Thesis"],"corr_author":"1","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"has_accepted_license":"1","article_processing_charge":"No","abstract":[{"text":"Many chemical and physical properties of materials are determined by the material’s shape,\r\nfor example the size of its pores and the width of its tunnels. This makes materials science\r\na prime application area for geometrical and topological methods. Nevertheless many\r\nmethods in topological data analysis have not been satisfyingly extended to the needs of\r\nmaterials science. This thesis provides new methods and new mathematical theorems\r\ntargeted at those specific needs by answering four different research questions. While the\r\nmotivation for each of the research questions arises from materials science, the methods\r\nare versatile and can be applied in different areas as well. \r\n\r\nThe first research question is concerned with image data, for example a three-dimensional\r\ncomputed tomography (CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies for digital images and depending on the application either of them might be\r\nrequired. However, software for computing the topological data analysis method persistence\r\nhomology, usually supports only one of the two topologies. We answer the question how to\r\ncompute persistent homology of an image with respect to one of the two topologies using\r\nsoftware that is intended for the other topology. \r\n\r\nThe second research question is concerned with image data as well, and asks how much\r\nof the topological information of an image is lost when the resolution is coarsened. As\r\ncomputer tomography scanners are more expensive the higher the resolution, it is an\r\nimportant question in materials science to know which resolution is enough to get satisfying\r\npersistent homology. We give theoretical bounds on the information loss based on different\r\ngeometrical properties of the object to be scanned. In addition, we conduct experiments on\r\nsand and stone CT image data. \r\n\r\nThe third research question is motivated by comparing crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically, crystalline materials are either modeled by\r\nunmanageable infinite periodic point sets, or by one of their fundamental domains, which is\r\nunstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate properties such that comparing the crystals can be eased by comparing the\r\nfingerprints instead. We define the density fingerprint and prove the necessary properties. \r\n\r\nThe fourth research question is motivated by studying the hole-structure or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials. A common way to deal\r\nwith periodicity is to take a fundamental domain and identify opposite boundaries to form a\r\ntorus. However, computing persistent homology or merge trees on that torus loses some\r\nof the information materials scientists are interested in and is additionally not stable under\r\ncertain noise. We therefore decorate the merge tree stemming from the torus with additional\r\ninformation describing the density and growth rate of the periodic copies of a component\r\nwithin a growing spherical window. We prove all desired properties, like stability and efficient\r\ncomputability.","lang":"eng"}],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-052-7"]},"doi":"10.15479/at:ista:18667","citation":{"ista":"Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria.","ieee":"T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024.","ama":"Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>","short":"T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024.","chicago":"Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>.","apa":"Heiss, T. (2024). <i>New methods for applying topological data analysis to materials science</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>","mla":"Heiss, Teresa. <i>New Methods for Applying Topological Data Analysis to Materials Science</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>."},"file_date_updated":"2024-12-19T10:24:50Z","title":"New methods for applying topological data analysis to materials science","ddc":["514","516","004"],"date_updated":"2026-10-02T11:55:42Z","_id":"18667","publisher":"Institute of Science and Technology Austria","degree_awarded":"PhD","acknowledgement":"I was supported by the European Research Council (ERC) Horizon 2020 project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship. In addition,\r\nI am very thankful for having been able to attend the second Workshop for Women in\r\nComputational Topology in July 2019, funded by the Mathematical Sciences Institute at\r\nANU, the US National Science Foundation through the award CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association for Women in Mathematics. Two of the\r\nprojects presented in this thesis started there. One of them reached completion thanks to\r\nfunding from the MSRI Summer Research in Mathematics program awarded to me and my\r\ncollaborators in 2020."}]