The mathematical and philosophical legacy of Alexander Grothendieck

• Titel: The mathematical and philosophical legacy of Alexander Grothendieck
• Mitwirkende: Panza, Marco [HerausgeberIn]
• Mitwirkende: Struppa, Daniele Carlo [HerausgeberIn]
• Mitwirkende: Szczeciniarz, Jean-Jacques [HerausgeberIn]
• Körperschaft: International Conference: Grothendieck, a multifarious giant: mathematics, logic and philosophy <2022, Orange, CA> [VerfasserIn]
• Verf.angabe: Marco Panza, Daniele C. Struppa, Jean-Jacques Szczeciniarz, editors
• Verlagsort: Cham
• Verlag: Birkhäuser
• E-Jahr: 2025
• Jahr: [2025]
• Umfang: 1 Online-Ressource (xvi, 512 Seiten)
• Gesamttitel/Reihe: Chapman mathematical notes
• ISBN: 978-3-031-68934-5
• DOI: doi:10.1007/978-3-031-68934-5
• Datenträger: Online-Ressource
• Dokumenttyp: Konferenzschrift
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe
• K10plus-PPN: 1915753619
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

Preface -- Grothendieck's 40 Main Years (1949-1991) -- Grothendieck and Differential Equations -- The Birkho-Grothendieck Theorem -- In nite Products, Congruent Numbers -- The Enduring Legacy of Grothenedieck's Duality Theorem -- Conjectures and Counterexamples in Grothendieck's Work in Functional Analysis -- Tohoku 60 years after -- About Grothendieck Fibrations.-Grothendieck did not Believe in Universes, He believed in Topos and Schemes -- Motivating Motives -- My View on and Experience with Grothendieck's Anabelian Geometry -- Grothendieck's Use of Equality -- Towards a Geometry for Syntax -- Boolean Valued Models, Sheafifications, and Boolean Ultrapowers of Tychono Spaces -- Investigating De nability in Propositional Logic -- Grothendieck and Model Theory -- Context-Dependence and Descent Theory -- Grothendieck and Teichmüller Modular Spaces.

Abstract

Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science.