/

Metric Algebraic Geometry

Breiding, Paul Kohn, Kathlén Sturmfels Bernd
Heftet / 2024 / Engelsk

Produktdetaljer

ISBN
9783031514616
Publisert
2024-02-28
Utgiver
Vendor
Birkhauser Verlag AG
Høyde
240 mm
Bredde
168 mm
Aldersnivå
Graduate, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet

Forfatter
Breiding, Paul
Kohn, Kathlén
Sturmfels Bernd

Biographical note

Paul Breiding is professor for mathematical methods in data science at the University of Osnabrück, an Emmy-Noether Research Group Leader and member of the Academy of Sciences and Literature Mainz. In 2021 he received the Early Career Prize of the SIAM Activity Group on Algebraic Geometry. His interests lie in numerical and random algebraic geometry. He is one of the developers of the software HomotopyContinuation.jl.

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.

Metric Algebraic Geometry

Breiding, Paul Kohn, Kathlén Sturmfels Bernd
Heftet / 2024 / Engelsk
Breiding, Paul Kohn, Kathlén Sturmfels Bernd
Heftet / 2024 / Engelsk
Nettpris:
685,-
Laveste pris siste 30 dager: 651,-
Levering 10-30 dager
Klikk og hent

<p>“The fifteen chapters of the book are well motivated and within reach of a motivated reader  with a moderate background in geometry and unrelated fields of application, for example, in probability theory or statistical models.” (Felipe Zaldiva, MAA Reviews, May 2, 2024)</p>

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.
Les mer
Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. 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.
Les mer
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.
Les mer
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.
Les mer
“The fifteen chapters of the book are well motivated and within reach of a motivated reader  with a moderate background in geometry and unrelated fields of application, for example, in probability theory or statistical models.” (Felipe Zaldiva, MAA Reviews, May 2, 2024)
Les mer
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
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer
Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Les mer

Relaterte produkter

<p>“The fifteen chapters of the book are well motivated and within reach of a motivated reader  with a moderate background in geometry and unrelated fields of application, for example, in probability theory or statistical models.” (Felipe Zaldiva, MAA Reviews, May 2, 2024)</p>

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.
Les mer
Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. 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.
Les mer
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.
Les mer
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.
Les mer
“The fifteen chapters of the book are well motivated and within reach of a motivated reader  with a moderate background in geometry and unrelated fields of application, for example, in probability theory or statistical models.” (Felipe Zaldiva, MAA Reviews, May 2, 2024)
Les mer
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
Les mer
GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
Les mer
Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Les mer

Produktdetaljer

ISBN
9783031514616
Publisert
2024-02-28
Utgiver
Vendor
Birkhauser Verlag AG
Høyde
240 mm
Bredde
168 mm
Aldersnivå
Graduate, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet

Forfatter
Breiding, Paul
Kohn, Kathlén
Sturmfels Bernd

Biographical note

Paul Breiding is professor for mathematical methods in data science at the University of Osnabrück, an Emmy-Noether Research Group Leader and member of the Academy of Sciences and Literature Mainz. In 2021 he received the Early Career Prize of the SIAM Activity Group on Algebraic Geometry. His interests lie in numerical and random algebraic geometry. He is one of the developers of the software HomotopyContinuation.jl.

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.

Relaterte produkter