Overview
- brings algebraic and differential geometry together in a computational setting
- provides a modern view on this connection, motivated by data science and AI
- focuses on concrete examples from a wide variety of applications
- This book is open access, which means that you have free and unlimited access
Part of the book series: Oberwolfach Seminars (OWS, volume 53)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
About the authors
Kathlén Kohn is a tenure-track assistant professor at KTH in Stockholm. Her research investigates the underlying geometry in computer-vision, machine-learning and statistical problems, using algebraic methods. For her research in computer vision, she received the Best Student Paper Award at the International Conference on Computer Vision (ICCV) in 2019 and the Swedish L'Oréal-Unesco for Women in Science prize in 2023.
After many years at UC Berkeley, Bernd Sturmfels now serves as a director at the Max-Planck Institute for Mathematics in the Sciences in Leipzig, Germany, where he leads the Nonlinear Algebra group. He has published 10 books and 300 articles, and he mentored 60 doctoral students, plus countless postdocs. His interests range from algebraic geometry and combinatorics to statistics, optimization and physics.
Bibliographic Information
Book Title: Metric Algebraic Geometry
Authors: Paul Breiding, Kathlén Kohn, Bernd Sturmfels
Series Title: Oberwolfach Seminars
DOI: https://doi.org/10.1007/978-3-031-51462-3
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s) 2024
Softcover ISBN: 978-3-031-51461-6Published: 28 February 2024
eBook ISBN: 978-3-031-51462-3Published: 27 February 2024
Series ISSN: 1661-237X
Series E-ISSN: 2296-5041
Edition Number: 1
Number of Pages: XIV, 215
Topics: Algebraic Geometry, Differential Geometry, Data Structures and Information Theory, Artificial Intelligence, Numerical Analysis