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Metric Algebraic Geometry

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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.

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Availability

Detail Information

Series Title

53

Call Number

-

Publisher

Cham : Birkhäuser Cham., 2024

Collation

XIV, 215

Language

English

ISBN/ISSN

9783031514623

Classification

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Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

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Subject(s)

Algebraic Geometry

Specific Detail Info

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Statement of Responsibility

Paul Breiding , Kathlén Kohn , Bernd Sturmfels

Other Information

Cataloger

Kholif Basri

Source

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Validator

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Digital Object Identifier (DOI)

https://doi.org/10.1007/978-3-031-51462-3

Journal Volume

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Journal Issue

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Subtitle

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Parallel Title

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