{"id":"https://openalex.org/G4222507278","display_name":"AF: Small: Expanding the Reach of Topological Data Analysis","description":"Data science and analysis have taken a center stage in modern years for a swath of applications\r\nembracing daily life. In general, AI and machine learning have been the backbone of this\r\ndevelopment. Recently, a technique based on the classical mathematical area of topology has evolved\r\nthat is showing promise to complement and in some cases be an alternative to AI techniques. As this\r\nemergent area, known as topological data analysis (TDA), expands its reach, the task of extracting\r\nintelligent summaries out of diverse, complex data becomes increasingly challenging. To meet this\r\nchallenge, TDA also needs to expand its current repertoire of techniques by making further and\r\ndeeper connections between mathematical and algorithmic concepts. This project aims to develop\r\nthese techniques while training graduate students and other workforce in data science as a\r\nconsequence.\r\n\r\nThe project, in particular, will investigate several novel mathematical concepts in conjunction with\r\ncomputations to address various challenges appearing in the following topics: (i) augmenting\r\ntopological summarization with geometry, (ii) connecting discrete Morse theory to further\r\napplications, (iii) developing persistence theory for combinatorial dynamical systems, and (iv)\r\ndeveloping multi-parameter persistence from a computational view-point. A successful algorithmic\r\ntheory supported by sound mathematics for the four aforementioned themes can provide a powerful\r\ntool for data exploration and analysis in a spectrum of engineering and scientific fields. The\r\nproposed outreach activities will also further consolidate the ongoing effort of bringing together\r\ndifferent communities in science and engineering engaged into modern data analysis. The project\r\nwill help train graduate students who will develop skills in mathematics and theoretical\r\ncomputer science, most notably in algorithms and topology, in writing efficient and usable software,\r\nand in its application to analyzing real-world data sets. Efforts will be made to recruit and mentor\r\nstudents from under-represented groups, as has already been done by the investigator.\r\n\r\nThis award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.","funder_award_id":"2049010","funder":{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","doi":"10.13039/100000001"},"funded_outputs":["https://openalex.org/W2990798340","https://openalex.org/W3135959378","https://openalex.org/W3208999859","https://openalex.org/W3215601401","https://openalex.org/W4220961412","https://openalex.org/W4221166092","https://openalex.org/W4224947531","https://openalex.org/W4226031082","https://openalex.org/W4281251613","https://openalex.org/W4289782736","https://openalex.org/W4310823343","https://openalex.org/W4385317150","https://openalex.org/W4390586483","https://openalex.org/W4391670500","https://openalex.org/W4392822318","https://openalex.org/W4393023600","https://openalex.org/W4399447945","https://openalex.org/W4399597812","https://openalex.org/W4404314231","https://openalex.org/W4410736738","https://openalex.org/W6966806356","https://openalex.org/W7172508320"],"funded_outputs_count":22,"parent_awards":[],"sub_awards":[],"sub_awards_count":0,"amount":350000.0,"currency":"USD","amount_usd":350000.0,"amount_usd_basis":"usd_native","recipients":[],"recipient_countries":[],"recipient_regions":[],"research_scope":{"is_research":true,"basis":"funder_default","tier":1},"funding_type":"grant","funder_scheme":"Standard Grant","start_date":"2020-08-15","end_date":"2024-08-31","start_year":2020,"end_year":2024,"landing_page_url":"https://www.nsf.gov/awardsearch/showAward?AWD_ID=2049010","doi":null,"provenance":"nsf_award_search","lead_investigator":{"given_name":"Tamal","family_name":"Dey","orcid":null,"role_start":null,"affiliation":{"name":"Purdue University","country":"United States","ids":null}},"co_lead_investigator":null,"investigators":null,"works_api_url":"https://api.openalex.org/works?filter=awards.id:G4222507278","primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9957,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9957,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"institution_awarded":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"updated_date":"2026-10-16T03:01:01.000Z","created_date":"2026-07-13T04:41:43.000Z"}