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Edited by: Eva Bayer-Fluckiger, CNRS, Université de Franche-Comte, Besançon, France, David Lewis, University College, Dublin, Ireland, and Andrew Ranicki, University of Edinburgh, Scotland
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Contemporary Mathematics
2000; 311 pp; softcover
Volume: 272
ISBN-10: 0-8218-2779-0
ISBN-13: 978-0-8218-2779-6
List Price: US$96 Member Price: US$76.80
Order Code: CONM/272

This volume outlines the proceedings of the conference on "Quadratic Forms and Their Applications" held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.

• E. Bayer-Fluckiger -- Galois cohomology of the classical groups
• A.-M. Bergé -- Symplectic lattices
• J. H. Conway -- Universal quadratic forms and the Fifteen Theorem
• M. Bhargava -- On the Conway-Schneeberger Fifteen Theorem
• M. Epkenhans -- On trace forms and the Burnside ring
• A. Fröhlich and C. T. C. Wall -- Equivariant Brauer groups
• D. W. Hoffmann -- Isotropy of quadratic forms and field invariants
• O. Izhboldin and A. Vishik -- Quadratic forms with absolutely maximal splitting
• A. F. Izmailov -- 2-regularity and reversibility of quadratic mappings
• C. Kearton -- Quadratic forms in knot theory
• I. Kersten -- Biography of Ernst Witt (1911-1991)
• M. Knebusch and U. Rehmann -- Generic splitting towers and generic splitting preparation of quadratic forms
• M. Mischler -- Local densities of hermitian forms
• V. Powers and B. Reznick -- Notes towards a constructive proof of Hilbert's theorem on ternary quartics
• W. Scharlau -- On the history of the algebraic theory of quadratic forms
• V. P. Snaith -- Local fundamental classes derived from higher $$K$$-groups: III
• R. G. Swan -- Hilbert's theorem on positive ternary quartics
• C. T. C. Wall -- Quadratic forms and normal surface singularities