
Award Number and Duration 
NSF DMS 2301361 (University of Utah) 
PIs 
Bei Wang (University of Utah, PI)
Facundo Mémoli (OSU, PI)
Tamal Dey (Perdue University, PI) 
Collaborators 
Kelin Xia, Associate Professor, School of Physical & Mathematical Sciences, Nanyang Technological University. 
Overview 
Complex datasets arise in many disciplines of science and engineering and require multiparameter data analysis, which broadly speaking, studies the dependency of a phenomenon or a space on multiple parameters. In recent years, topological data analysis (TDA) has evolved as an emerging area in data science. So far, most of its applications have been limited to the single parameter case, that is, to data expressing the behavior of a single variable. As its reach to applications expands, the task of extracting intelligent summaries out of diverse, complex data demands the study of multiparameter dependencies. This project will help address this demand. 
Broader Impacts 
This project will develop a sound mathematical theory supported by efficient algorithmic tools for the aforementioned thrusts and, thus, will provide a powerful platform for data exploration and analysis in a range of applications in science and engineering. The educational impact will be accelerated by the synergy between mathematics and computer science and integrated applications. Graduate students supported by the project will be trained to: develop skills in mathematics and theoretical computer science, most notably in algorithms and topology, write efficient and usable software, and analyze realworld data sets. The PIs will provide best practice recruiting and mentoring of students from underrepresented groups. The PIs plan to broaden research engagement via workshops or tutorials at computational topology and TDA venues. A nationally focused hackathon will introduce methodologies and software tools for multiparameter TDA to the research community as where participants work on data analysis projects while being mentored by disciplinary experts. The outreach activities including a K12 summer camp and a data science day will further converge disciplinary communities and introduce high school students to novel modern data analysis. 
Publications and Manuscripts 
Year 1 (2023  2024)  
MeasureTheoretic Reeb Graphs and Reeb Spaces.
Qingsong Wang, Guanquan Ma, Raghavendra Sridharamurthy, Bei Wang. International Symposium on Computational Geometry (SOCG), 2024. DOI:10.4230/LIPIcs.SoCG.2024.80 arXiv:2401.06748.  
PersiSort: A New Perspective on Adaptive Sorting Based on Persistence.
Jens Kristian Refsgaard Schou, Bei Wang. Proceedings of the 36th Canadian Conference on Computational Geometry (CCCG), 2024.  
A Survey of Simplicial, Relative, and Chain
Complex Homology Theories for Hypergraphs.
Ellen Gasparovic, Emilie Purvine, Radmila Sazdanovic, Bei Wang, Yusu Wang, Lori Ziegelmeier. Manuscript, 2024.  
Computing Loss Function to Bound the Interleaving Distance for Mapper Graphs (Abstract).
Erin Wolf Chambers, Ishika Ghosh, Elizabeth Munch, Sarah Percival, Bei Wang. International Symposium on Computational Geometry (SOCG) Young Researcher Forum (YRF), 2024.  
Harmonic Chain Barcode and Stability.
Salman Parsa and Bei Wang. Manuscript, 2024.  
Bounding the Interleaving Distance for Mapper Graphs with a Loss
Function.
Erin W. Chambers, Elizabeth Munch, Sarah Percival, Bei Wang. Manuscript, 2023. arXiv:2307.15130 
Presentations, Educational Development and Broader Impacts 
Year 1 (2023  2024) 

Postdocs and Students 
Qingsong Wang (Mathematics Postdoc) 
Acknowledgement 
This material is based upon work supported or partially supported by the National Science Foundation under Grant No. 2301361. 