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Article: Machine Learning Assisted Exploration for Affine Deligne–Lusztig Varieties

TitleMachine Learning Assisted Exploration for Affine Deligne–Lusztig Varieties
Authors
Issue Date15-May-2024
PublisherSpringer
Citation
Peking Mathematical Journal, 2024, v. 7, n. 2 How to Cite?
Abstract

This paper presents a novel, interdisciplinary study that leverages a Machine Learning (ML) assisted framework to explore the geometry of affine Deligne–Lusztig varieties (ADLV). The primary objective is to investigate the non-emptiness pattern, dimension, and enumeration of irreducible components of ADLV. Our proposed framework demonstrates a recursive pipeline of data generation, model training, pattern analysis, and human examination, presenting an intricate interplay between ML and pure mathematical research. Notably, our data-generation process is nuanced, emphasizing the selection of meaningful subsets and appropriate feature sets. We demonstrate that this framework has a potential to accelerate pure mathematical research, leading to the discovery of new conjectures and promising research directions that could otherwise take significant time to uncover. We rediscover the virtual dimension formula and provide a full mathematical proof of a newly identified problem concerning a certain lower bound of dimension. Furthermore, we extend an open invitation to the readers by providing the source code for computing ADLV and the ML models, promoting further explorations. This paper concludes by sharing valuable experiences and highlighting lessons learned from this collaboration.


Persistent Identifierhttp://hdl.handle.net/10722/347540
ISSN

 

DC FieldValueLanguage
dc.contributor.authorDong, Bin-
dc.contributor.authorHe, Xuhua-
dc.contributor.authorJin, Pengfei-
dc.contributor.authorSchremmer, Felix-
dc.contributor.authorYu, Qingchao-
dc.date.accessioned2024-09-25T00:30:37Z-
dc.date.available2024-09-25T00:30:37Z-
dc.date.issued2024-05-15-
dc.identifier.citationPeking Mathematical Journal, 2024, v. 7, n. 2-
dc.identifier.issn2096-6075-
dc.identifier.urihttp://hdl.handle.net/10722/347540-
dc.description.abstract<p>This paper presents a novel, interdisciplinary study that leverages a Machine Learning (ML) assisted framework to explore the geometry of affine Deligne–Lusztig varieties (ADLV). The primary objective is to investigate the non-emptiness pattern, dimension, and enumeration of irreducible components of ADLV. Our proposed framework demonstrates a recursive pipeline of data generation, model training, pattern analysis, and human examination, presenting an intricate interplay between ML and pure mathematical research. Notably, our data-generation process is nuanced, emphasizing the selection of meaningful subsets and appropriate feature sets. We demonstrate that this framework has a potential to accelerate pure mathematical research, leading to the discovery of new conjectures and promising research directions that could otherwise take significant time to uncover. We rediscover the virtual dimension formula and provide a full mathematical proof of a newly identified problem concerning a certain lower bound of dimension. Furthermore, we extend an open invitation to the readers by providing the source code for computing ADLV and the ML models, promoting further explorations. This paper concludes by sharing valuable experiences and highlighting lessons learned from this collaboration.<br></p>-
dc.languageeng-
dc.publisherSpringer-
dc.relation.ispartofPeking Mathematical Journal-
dc.titleMachine Learning Assisted Exploration for Affine Deligne–Lusztig Varieties-
dc.typeArticle-
dc.identifier.doi10.1007/s42543-024-00086-8-
dc.identifier.volume7-
dc.identifier.issue2-
dc.identifier.eissn2524-7182-
dc.identifier.issnl2524-7182-

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