Metric Algebraic Geometry
Breiding, Paul, Kohn, Kathlén, Sturmfels, Bernd
- 出版商: Birkhauser Boston
- 出版日期: 2024-02-28
- 售價: $2,230
- 貴賓價: 9.5 折 $2,119
- 語言: 英文
- 頁數: 215
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031514610
- ISBN-13: 9783031514616
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商品描述
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.
作者簡介
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.
