{"title":"Stefan Mllerstach","description":null,"products":[{"product_id":"period-mappings-and-period-domains-book-james-carlson-9781316639566","title":"Period Mappings and Period Domains","description":"The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a two-torus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelov-type theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50159396126993,"sku":"CIN1316639568G","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52593606623505,"sku":"NLS9781316639566","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1316639568.jpg?v=1751207686"},{"product_id":"code-of-mathematics-book-stefan-mllerstach-9783662694824","title":"The Code of Mathematics","description":"Inspired by recent developments in dependent type theory and infinity categories, this book presents a history of ideas around the topics of truth, proof, equality and equivalence. The main focus of this textbook is on dependent type theory and its recent variant homotopy type theory.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":50406758875409,"sku":"NGR9783662694824","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51061099168017,"sku":"NIN9783662694824","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52656876454161,"sku":"NLS9783662694824","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3662694824.jpg?v=1770285560"},{"product_id":"elementare-und-algebraische-zahlentheorie-book-stefan-mllerstach-9783834812568","title":"Elementare und algebraische Zahlentheorie","description":"Das Buch wendet sich an alle, die in die klassischen Themen der Zahlentheorie einsteigen wollen. Neben den Standardthemen wie Primzahlen, Rechnen modulo n, quadratische Reste und Kettenbrüche werden auch die fortgeschrittenen Bereiche wie p-adische Zahlen, quadratische Formen und Zahlkörper am Beispiel der quadratischen Zahlkörper behandelt. Viel Wert wird auf die konkrete Berechenbarkeit bei allen Problemlösungen gelegt. \u003cbr\u003e\nIm Rahmen der Bachelor-\/Master-Studiengänge eignet sich das Buch als Grundlage für zwei Semester: ein Aufbaumodul in elementarer Zahlentheorie mit einem Vertiefungsmodul in algebraischer Zahlentheorie. \u003cbr\u003e\nDie zweite Auflage enthält neben Verbesserungen viele neue Übungsaufgaben mit  Lösungen oder Lösungshinweisen. Außerdem wurde ein Anhang über die Minkowski-Theorie ergänzt.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51123371016465,"sku":"NIN9783834812568","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52125953065233,"sku":"NLS9783834812568","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3834812560.jpg?v=1792020580"},{"product_id":"richard-dedekind-book-stefan-mllerstach-9783662700563","title":"Richard Dedekind","description":"\u003cp\u003eThe two works titled \"What Are and What Should the Numbers Be?\" (1888) and \"Continuity and Irrational Numbers\" (1872) are Dedekind's contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind's achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today.\u003c\/p\u003e\n\n\u003cp\u003eThis volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind's pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann.\u003c\/p\u003e\n\n\u003cp\u003eResearchers and students alike will find this work a valuable reference in the history of mathematics.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51717801640209,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51717803016465,"sku":"NGR9783662700563","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3662700565.jpg?v=1793352275"},{"product_id":"richard-dedekind-book-stefan-mllerstach-9783662681411","title":"Richard Dedekind","description":"Die beiden Bücher „Was sind und was sollen die Zahlen?“ (1888) und „Stetigkeit und Irrationale Zahlen“ (1872) sind Dedekinds Beiträge zu den Grundlagen der Mathematik; er legte darin die  Grundsteine der Mengenlehre und der Theorie der reellen und natürlichen Zahlen. Diese Schriften sind aus der modernen Mathematik nicht mehr wegzudenken. Dennoch wurde die Leistung Dedekinds nicht immer entsprechend gewürdigt und der Inhalt dieser Bücher ist auch heute noch vielen Mathematikerinnen und Mathematikern wenig bekannt. \u003cbr\u003e Dieses Buch enthält neben den Originaltexten eine ausführliche Erklärung der beiden Schriften und eine Interpretation in moderner Sprache, sowie eine kurze Biografie und eine Abschrift des berühmten Briefs an H. Keferstein. Dadurch bietet dieses Buch einen faszinierenden Einblick in das Leben und Schaffen dieses wegweisenden Wissenschaftlers und stellt sein Werk in Beziehung zu großen Zeitgenossen wie Cantor, Dirichlet, Frege, Hilbert, Kronecker und Riemann.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52347080474897,"sku":"NLS9783662681411","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783662681411.jpg?v=1785801931"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-stefan-mllerstach.oembed","provider":"World of Books ","version":"1.0","type":"link"}