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Duality in 19th and 20th Century Mathematical Thinking / / edited by Ralf Krömer, Emmylou Haffner
| Duality in 19th and 20th Century Mathematical Thinking / / edited by Ralf Krömer, Emmylou Haffner |
| Edizione | [1st ed. 2024.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2024 |
| Descrizione fisica | 1 online resource (962 pages) |
| Disciplina | 510.9034 |
| Collana | Science Networks. Historical Studies |
| Soggetto topico |
Mathematics
History Algebra, Homological Algebra, Universal History of Mathematical Sciences Category Theory, Homological Algebra General Algebraic Systems Corbes Teoria de la dualitat (Matemàtica) Topologia Història de la matemàtica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031597978
3031597974 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Chapter 1. Ralf Krömer, Emmylou Haffner: Introduction -- Part I. The 19th century heritage -- Chapter 2. Michael Friedman: On “contour apparent”, “courbe de contact” and ramification curves: Duality between a principle and a tool -- Chapter 3. Juan Luis Gastaldi: De Morgan’s De Morgan’s Laws: Duality in the Emergence of Formal Logic -- Chapter 4. Dirk Schlimm: The emergence of duality in 19th-century algebra of logic -- Chapter 5. Emmylou Haffner: Duality as a guiding light in the genesis of Dedekind’s Dualgruppen -- Chapter 6. Erhard Scholz: From Grassmann complements to Hodge-duality -- Part II. From topology to groups -- Chapter 7. Stephan Oltmanns, Ralf Krömer, Klaus Volkert: Duality theorems in topology -- Chapter 8. Ralf Krömer: The historical development of Pontrjagin duality -- Chapter 9. Harald Kümmerle: Tannaka Tadao’s 1938 paper on the duality of noncommutative topological groups and its historical background -- Chapter 10. Christophe Eckes: Philosophical and mathematical duality in Albert Lautman’s work -- Part III. Functional analysis and related fields -- Chapter 11. Alessa Waldvogel: The development of dual spaces in functional analysis -- Chapter 12. Frédéric Jaëck: Duality in Banach’s 1929 work on functionals -- Chapter 13. Ralf Krömer: Marshall Stone and duality: from differential equations to Boolean algebras -- Chapter 14. Ralf Krömer: Duality à la Bourbaki -- Chapter 15. Jesper Lützen: Duality and Distributions: An Application of Topological Vector Spaces -- Part IV. The post-war outlook -- Chapter 16. Tinne Hoff Kjeldsen: From duality in mathematical programming to Fenchel duality and convex analysis: Duality as a force of inspiration in the creation of new mathematics -- Chapter 17. Jean-Pierre Marquis: An Historical Perspective on Duality and Category Theory -- List of abbreviations -- Bibliography -- Author index. |
| Record Nr. | UNINA-9910869169903321 |
| Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier
| Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier |
| Autore | Erlandsson Viveka |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (233 pages) |
| Disciplina | 516.352 |
| Collana | Progress in Mathematics |
| Soggetto topico |
Curves, Algebraic
Curves, Algebraic - Data processing Corbes Corbes algebraiques |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-08705-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgments -- Contents -- Notation -- 1 Introduction -- Some Things that the Reader Will Not Find in This Book -- What the Reader Will Find Here -- A Comment on the Way This Book Is Written -- 2 Read Me -- Curves, Multicurves, and Arcs -- Intersection Number -- Geodesic Representatives -- Random Geodesics. Or Length Versus Intersections -- Space of Geodesics -- Geodesics Projecting into a Fixed Compact Set -- Laminations -- Hausdorff Limits -- Mapping Class Group -- Shortening Curves -- 3 Geodesic Currents -- Definition and Examples -- Curves as Currents -- Weighted Multicurves -- Measured Laminations -- The Space of Geodesic Currents -- Interesting Subsets of C(Σ) -- Intersection Form -- Characterization of Measured Laminations -- Filling Currents -- The Mapping Class Group Action -- Mapping Class Group Action on the Set of Filling Currents -- Comments (The Liouville Current) -- 4 Train Tracks -- Train Tracks as Smoothly Embedded Complexes -- Almost Geodesic Train Tracks -- Band Complexes and Train Tracks -- Curves and Laminations Carried by Train Tracks -- Weights and Recurrence -- Switch Equations -- Thurston Measure -- First Counting Result -- Masur's Ergodicity Theorem -- An Example: The Case of the Once Punctured Torus -- Comments -- Piecewise Linear Structure -- Symplectic Structure -- Weil-Petersson Volume Form -- Other Interesting Measures on ML(S) -- 5 Radallas -- Terminology -- The Game of Cars -- Almost Geodesic Radallas -- Finding Almost Geodesic Radallas -- Generic Curves -- Comments: Expected Angle of Self-Intersection -- 6 Subconvergence of Measures -- Idea of the Proof of Theorem 6.1 -- Local Map -- Global Map -- New Measures -- Comments -- 7 Approximating the Thurston Measure -- Dribbling -- Radallas Carrying the Curves in Θσ0 -- Reducing to a Linear Algebra Problem -- Proof of Proposition 7.2.
Comments -- 8 The Main Theorem -- Notation and the Constants -- The Theorem -- The Fundamental Domain -- The Meat -- The Not Ker-Invariant Case -- Comments -- 9 Counting Curves -- Main Curve Counting Theorem -- Frequencies and Relative Frequencies -- Functions on the Space of Currents -- 10 Counting Square-Tiled Surfaces -- Square-Tiled Surfaces -- Recovering Square-Tiled Surface Structures from Multicurves -- Square-Tiled Surfaces of Given Type -- Counting -- Comments -- 11 Statistics of Simple Curves -- Credit to Kasra -- Hard Data -- A Formula for c(α0) for Simple Curves -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-Separating Curves in Closed Surfaces -- Combinatorial Computation -- Changing Weights -- Comments -- 12 Smörgåsbord -- Random Pants Decompositions -- Lattice Point Counting in Teichmüller Space -- Genericty of pseudo-Anosov Elements -- A Radon Measures -- Point-Set Topology -- Weak-*-Topology -- Sequential Compactness -- B Computing Thurston Volumes -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-separating Curves in Closed Surfaces -- References -- Index. |
| Record Nr. | UNISA-996490345903316 |
Erlandsson Viveka
|
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| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier
| Mirzakhani's curve counting and geodesic currents / / Viveka Erlandsson, Juan Souto, and Hugo Parlier |
| Autore | Erlandsson Viveka |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer International Publishing, , [2022] |
| Descrizione fisica | 1 online resource (233 pages) |
| Disciplina | 516.352 |
| Collana | Progress in Mathematics |
| Soggetto topico |
Curves, Algebraic
Curves, Algebraic - Data processing Corbes Corbes algebraiques |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-08705-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgments -- Contents -- Notation -- 1 Introduction -- Some Things that the Reader Will Not Find in This Book -- What the Reader Will Find Here -- A Comment on the Way This Book Is Written -- 2 Read Me -- Curves, Multicurves, and Arcs -- Intersection Number -- Geodesic Representatives -- Random Geodesics. Or Length Versus Intersections -- Space of Geodesics -- Geodesics Projecting into a Fixed Compact Set -- Laminations -- Hausdorff Limits -- Mapping Class Group -- Shortening Curves -- 3 Geodesic Currents -- Definition and Examples -- Curves as Currents -- Weighted Multicurves -- Measured Laminations -- The Space of Geodesic Currents -- Interesting Subsets of C(Σ) -- Intersection Form -- Characterization of Measured Laminations -- Filling Currents -- The Mapping Class Group Action -- Mapping Class Group Action on the Set of Filling Currents -- Comments (The Liouville Current) -- 4 Train Tracks -- Train Tracks as Smoothly Embedded Complexes -- Almost Geodesic Train Tracks -- Band Complexes and Train Tracks -- Curves and Laminations Carried by Train Tracks -- Weights and Recurrence -- Switch Equations -- Thurston Measure -- First Counting Result -- Masur's Ergodicity Theorem -- An Example: The Case of the Once Punctured Torus -- Comments -- Piecewise Linear Structure -- Symplectic Structure -- Weil-Petersson Volume Form -- Other Interesting Measures on ML(S) -- 5 Radallas -- Terminology -- The Game of Cars -- Almost Geodesic Radallas -- Finding Almost Geodesic Radallas -- Generic Curves -- Comments: Expected Angle of Self-Intersection -- 6 Subconvergence of Measures -- Idea of the Proof of Theorem 6.1 -- Local Map -- Global Map -- New Measures -- Comments -- 7 Approximating the Thurston Measure -- Dribbling -- Radallas Carrying the Curves in Θσ0 -- Reducing to a Linear Algebra Problem -- Proof of Proposition 7.2.
Comments -- 8 The Main Theorem -- Notation and the Constants -- The Theorem -- The Fundamental Domain -- The Meat -- The Not Ker-Invariant Case -- Comments -- 9 Counting Curves -- Main Curve Counting Theorem -- Frequencies and Relative Frequencies -- Functions on the Space of Currents -- 10 Counting Square-Tiled Surfaces -- Square-Tiled Surfaces -- Recovering Square-Tiled Surface Structures from Multicurves -- Square-Tiled Surfaces of Given Type -- Counting -- Comments -- 11 Statistics of Simple Curves -- Credit to Kasra -- Hard Data -- A Formula for c(α0) for Simple Curves -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-Separating Curves in Closed Surfaces -- Combinatorial Computation -- Changing Weights -- Comments -- 12 Smörgåsbord -- Random Pants Decompositions -- Lattice Point Counting in Teichmüller Space -- Genericty of pseudo-Anosov Elements -- A Radon Measures -- Point-Set Topology -- Weak-*-Topology -- Sequential Compactness -- B Computing Thurston Volumes -- Punctured Spheres -- Separating Curves in Closed Surfaces -- Non-separating Curves in Closed Surfaces -- References -- Index. |
| Record Nr. | UNINA-9910595045203321 |
|
Erlandsson Viveka
|
||
| Cham, Switzerland : , : Springer International Publishing, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
