LEADER 03412nam 22006975 450 001 9910842097003321 005 20241120175004.0 010 $a3-031-51462-9 024 7 $a10.1007/978-3-031-51462-3 035 $a(CKB)30597528200041 035 $a(MiAaPQ)EBC31323953 035 $a(Au-PeEL)EBL31323953 035 $a(OCoLC)1425878264 035 $a(DE-He213)978-3-031-51462-3 035 $a(EXLCZ)9930597528200041 100 $a20240227d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMetric Algebraic Geometry /$fby Paul Breiding, Kathlén Kohn, Bernd Sturmfels 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (225 pages) 225 1 $aOberwolfach Seminars,$x2296-5041 ;$v53 311 $a3-031-51461-0 327 $aPreface -- 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. 330 $aMetric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances. After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety. This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an open access book. 410 0$aOberwolfach Seminars,$x2296-5041 ;$v53 606 $aGeometry, Algebraic 606 $aGeometry, Differential 606 $aArtificial intelligence$xData processing 606 $aNumerical analysis 606 $aAlgebraic Geometry 606 $aDifferential Geometry 606 $aData Science 606 $aNumerical Analysis 606 $aGeometria algebraica$2thub 608 $aCongressos$2thub 608 $aLlibres electrònics$2thub 615 0$aGeometry, Algebraic. 615 0$aGeometry, Differential. 615 0$aArtificial intelligence$xData processing. 615 0$aNumerical analysis. 615 14$aAlgebraic Geometry. 615 24$aDifferential Geometry. 615 24$aData Science. 615 24$aNumerical Analysis. 615 7$aGeometria algebraica 676 $a516.35 700 $aBreiding$b Paul$01736940 701 $aKohn$b Kathlén$01736941 701 $aSturmfels$b Bernd$054580 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910842097003321 996 $aMetric Algebraic Geometry$94157838 997 $aUNINA