Metric algebraic geometry

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 i...

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Hlavní autoři: Breiding, Paul, Kohn, Kathlén, Sturmfels, Bernd
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Cham Springer Nature Switzerland AG 2024
Birkhäuser
Springer Nature
Birkhäuser Boston
Vydání:1
Edice:Oberwolfach Seminars
Témata:
Algebraic geometry
Algebraic Variety
Artificial intelligence
Calculus and mathematical analysis
Computing and Information Technology
Curvature
Data Science
Differential and Riemannian geometry
Differential Geometry
Euclidean Distance
Geometry
Geometry, Differential
Integrals
Mathematics
Mathematics and Science
Maximum Likelihood
Numerical analysis
Numerical Methods
Polynomial Optimization
Polynomial System
Tensors
ISBN:9783031514616, 3031514610, 9783031514623, 3031514629
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Popis
Shrnutí: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 openaccess book.
Bibliografie:Includes bibliographical references
ISBN:9783031514616
3031514610
9783031514623
3031514629
DOI:10.1007/978-3-031-51462-3