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＜電子ブック＞
Metric Algebraic Geometry / by Paul Breiding, Kathlén Kohn, Bernd Sturmfels
(Oberwolfach Seminars. ISSN:22965041 ; 53)

版	1st ed. 2024.
出版者	(Cham : Springer Nature Switzerland : Imprint: Birkhäuser)
出版年	2024
本文言語	英語
大きさ	XIV, 215 p : online resource
著者標目	*Breiding, Paul author Kohn, Kathlén author Sturmfels, Bernd author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Geometry, Differential LCSH:Artificial intelligence -- Data processing  全ての件名で検索 LCSH:Numerical analysis FREE:Algebraic Geometry FREE:Differential Geometry FREE:Data Science FREE:Numerical Analysis
一般注記	Preface -- Historical Snapshot -- Critical Equations -- Computations -- Polar Degrees -- Wasserstein Distance -- Curvature -- Reach and Offset -- Voronoi Cells -- Condition Numbers -- Machine Learning -- Maximum Likelihood -- Tensors -- Computer Vision -- Volumes of Semialgebraic Sets -- Sampling -- References Open Access Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety. This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an open access book HTTP:URL=https://doi.org/10.1007/978-3-031-51462-3

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