Isaac Ren

I am a math PhD student at KTH Royal Institute of Technology in Stockholm, under the supervision of Assistant Professor Martina Scolamiero. My official profile page is here.

My research interests include Topological Data Analysis and homological algebra. I have also worked on linear rewriting theory and computational aspects of knot homology.

I have previously studied at École Normale Supérieure de Lyon and Lycée Louis le Grand. I speak English and French.

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Preprints & publications

Preprints

• "Koszul complexes and relative homological algebra of functors over posets," with Wojciech Chachólski, Andrea Guidolin, Martina Scolamiero, and Francesca Tombari, 2022. Submitted.
• "Algebraic Wasserstein distances and stable homological invariants of data," with Jens Agerberg, Andrea Guidolin, and Martina Scolamiero, 2023. Submitted.
• "Morse theory of Euclidean distance functions and applications to real algebraic geometry," with Andrea Guidolin, Antonio Lerario, and Martina Scolamiero, 2024.

Journal publications

• "Shuffle polygraphic resolutions for operads," with Philippe Malbos, Journal of the London Mathematical Society, Volume 107, Issue 1, pp. 61-122, 2023. arXiv version.

Conference papers

• "Completion of operadic rewriting systems by Gaussian elimination," with Benjamin Dupont and Philippe Malbos, Proceedings of the 10th International Workshop on Confluence (IWC 2021), 15-23. July 2021.
• "Completion in Operads via Syzygies," with Philippe Malbos, Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation (ISSAC '21), 305–312. Association for Computing Machinery, New York, NY, USA. July 2021.

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Conferences & seminars

• "Computing relative Betti diagrams of multipersistence modules using Koszul complexes," JMM 2024 AMS Special Session on Applied Topology: Theory, Algorithms, and Applications, January 5, 2024. San Francisco, USA: slides.
• "Computing relative homological invariants of persistence modules using Koszul complexes," Young Topologist Meeting 2023, July 24, 2023. EPFL, Lausanne, Switzerland: slides, video from a similar talk at ComPer 2023.
• "Computational examples of relative Betti diagrams," Interactions between representation theory and topological data analysis, December 8, 2022. Center for Advanced Studies, Oslo, Norway. slides.
• "Relative homological algebra and Koszul complexes for persistence modules," 2nd Young Topologist Seminar, July 7, 2022. Online: slides.
• "Completion of operadic rewriting systems by Gaussian elimination," with Benjamin Dupont, 10th International Workshop on Confluence (IWC 2021), July 23, 2021. Online: video.
• "Completion in Operads via Syzygies," International Symposium on Symbolic and Algebraic Computation (ISSAC 2021), July 22, 2021. Online.
• "Higher dimensional polygraphs and operadic rewriting," Categories and Companions Symposium 2021, June 9, 2021. Online: video.
• "Operadic rewriting and Koszulness," Algebraic rewriting seminar, March 18, 2021. Online: video, slides.
• "Operadic rewriting and Koszulness," Institut Camille Jordan algebra seminar, February 25, 2021. Online.
• "Rewriting in shuffle operads and resolutions of operads," Journées Logique, Homotopie, Catégories 2020/2021, February 5, 2021. Online: slides.