The embedded homology of hypergraphs on manifolds and configuration spaces

Shiquan Ren
Proceedings of the Geometry, Topology, and Machine Learning Workshop, PMLR 325:262-268, 2026.

Abstract

In this article, we give a short survey on the embedded homology of hypergraphs, random hypergraphs, and hypergraphs on manifolds by S. Bressan, J. Li, S. Ren, C. Wu, J. Wu, M. Zhang et al. from 2019 to 2025. We review the motivating problems as well as the meanings for the embedded homology of hypergraphs, the map algebra of hypergraphs, the relations between random hypergraphs and random simplicial complexes, and the double complexes for hypergraphs on manifolds. Besides, we give some further discussions about potential applications of hypergraphs on manifolds in the $r$-ball packing problems and the $r$-ball covering problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v325-ren26a, title = {The embedded homology of hypergraphs on manifolds and configuration spaces}, author = {Ren, Shiquan}, booktitle = {Proceedings of the Geometry, Topology, and Machine Learning Workshop}, pages = {262--268}, year = {2026}, editor = {Bleher, Michael and Jensen, Freya and Maier, Levin and Taha, Diaaeldin and Wienhard, Anna}, volume = {325}, series = {Proceedings of Machine Learning Research}, month = {10--14 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v325/main/assets/ren26a/ren26a.pdf}, url = {https://proceedings.mlr.press/v325/ren26a.html}, abstract = {In this article, we give a short survey on the embedded homology of hypergraphs, random hypergraphs, and hypergraphs on manifolds by S. Bressan, J. Li, S. Ren, C. Wu, J. Wu, M. Zhang et al. from 2019 to 2025. We review the motivating problems as well as the meanings for the embedded homology of hypergraphs, the map algebra of hypergraphs, the relations between random hypergraphs and random simplicial complexes, and the double complexes for hypergraphs on manifolds. Besides, we give some further discussions about potential applications of hypergraphs on manifolds in the $r$-ball packing problems and the $r$-ball covering problems.} }
Endnote
%0 Conference Paper %T The embedded homology of hypergraphs on manifolds and configuration spaces %A Shiquan Ren %B Proceedings of the Geometry, Topology, and Machine Learning Workshop %C Proceedings of Machine Learning Research %D 2026 %E Michael Bleher %E Freya Jensen %E Levin Maier %E Diaaeldin Taha %E Anna Wienhard %F pmlr-v325-ren26a %I PMLR %P 262--268 %U https://proceedings.mlr.press/v325/ren26a.html %V 325 %X In this article, we give a short survey on the embedded homology of hypergraphs, random hypergraphs, and hypergraphs on manifolds by S. Bressan, J. Li, S. Ren, C. Wu, J. Wu, M. Zhang et al. from 2019 to 2025. We review the motivating problems as well as the meanings for the embedded homology of hypergraphs, the map algebra of hypergraphs, the relations between random hypergraphs and random simplicial complexes, and the double complexes for hypergraphs on manifolds. Besides, we give some further discussions about potential applications of hypergraphs on manifolds in the $r$-ball packing problems and the $r$-ball covering problems.
APA
Ren, S.. (2026). The embedded homology of hypergraphs on manifolds and configuration spaces. Proceedings of the Geometry, Topology, and Machine Learning Workshop, in Proceedings of Machine Learning Research 325:262-268 Available from https://proceedings.mlr.press/v325/ren26a.html.

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