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dc.contributor.authorBreiding, Paul
dc.contributor.authorKohn, Kathlén
dc.contributor.authorSturmfels, Bernd
dc.date.accessioned2024-03-13T11:11:13Z
dc.date.available2024-03-13T11:11:13Z
dc.date.issued2024
dc.identifierONIX_20240313_9783031514623_48
dc.identifier.urihttps://library.oapen.org/handle/20.500.12657/88360
dc.description.abstractMetric 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.
dc.languageEnglish
dc.relation.ispartofseriesOberwolfach Seminars
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMW Algebraic geometryen_US
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PB Mathematics::PBM Geometry::PBMP Differential and Riemannian geometryen_US
dc.subject.classificationthema EDItEUR::U Computing and Information Technology::UN Databasesen_US
dc.subject.classificationthema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKS Numerical analysisen_US
dc.subject.otherAlgebraic Variety
dc.subject.otherData Science
dc.subject.otherDifferential Geometry
dc.subject.otherEuclidean Distance
dc.subject.otherIntegrals
dc.subject.otherMaximum Likelihood
dc.subject.otherNumerical Methods
dc.subject.otherPolynomial System
dc.subject.otherTensors
dc.subject.otherCurvature
dc.subject.otherPolynomial Optimization
dc.titleMetric Algebraic Geometry
dc.typebook
oapen.identifier.doi10.1007/978-3-031-51462-3
oapen.relation.isPublishedBy6c6992af-b843-4f46-859c-f6e9998e40d5
oapen.relation.isFundedBy8e7742bc-c35e-4523-8581-875fb10bfc5e
oapen.relation.isFundedByd880bcc0-ecff-409c-9896-c00d438cc124
oapen.relation.isbn9783031514623
oapen.relation.isbn9783031514616
oapen.imprintBirkhäuser
oapen.series.number53
oapen.pages215
oapen.place.publicationCham
oapen.grant.number[...]
oapen.grant.number[...]


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