Quadratic Forms and Their Applications: Proceedings of the Conference on Quadratic Forms and Their Applications, July 5-9, 1999, University College Dublin (Contemporary Mathematics)

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. Readership:Graduate students and research mathematicians interested in quadratic forms. Galois Cohomology Of The Classical Groups / Eva Bayer-fluckiger -- Symplectic Lattices / Anne-marie Berge -- Universal Quadratic Forms And The Fifteen Theorem / J. H. Conway -- On The Conway-schneeberger Fifteen Theorem / Manjul Bhargava -- On Trace Forms And The Burnside Ring / Martin Epkenhans -- Equivariant Brauer Groups / A. Frohlich And C. T. C. Wall -- Isotropy Of Quadratic Forms And Field Invariants / Detlev W. Hoffmann -- Quadratic Forms With Absolutely Maximal Splitting / Oleg Izhboldin And Alexander Vishik -- 2-regularity And Reversibility Of Quadratic Mappings / Alexey F. Izmailov -- Quadratic Forms In Knot Theory / C. Kearton -- Biography Of Ernst Witt (1911-1991) / Ina Kersten -- Generic Splitting Towers And Generic Splitting Preparation Of Quadratic Forms / Manfred Knebusch And Ulf Rehmann -- Local Densities Of Hermitian Forms / Maurice Mischler -- Notes Towards A Constructive Proof Of Hilbert's Theorem On Ternary Quartics / Victoria Powers And Bruce Reznick -- On The History Of The Algebraic Theory Of Quadratic Forms / Winfried Scharlau -- Local Fundamental Classes Derived From Higher K-groups: Iii / Victor P. Snaith -- Hilbert's Theorem On Positive Ternary Quartics / Richard G. Swan -- Quadratic Forms And Normal Surface Singularities / C. T. C. Wall. Eva Bayer-fluckiger, David Lewis, Andrew Ranicki, Editors. Includes Bibliographical References (p.310-311). 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 Outlines the proceedings of the conference on 'Quadratic Forms and Their Applications' held at University College Dublin. This work includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history.