Contemporary Mathematics 2004; 350 pp; softcover Volume: 344 ISBN10: 082183441X ISBN13: 9780821834411 List Price: US$98 Member Price: US$78.40 Order Code: CONM/344
 This proceedings volume contains papers presented at the International Conference on the algebraic and arithmetic theory of quadratic forms held in Talca (Chile). The modern theory of quadratic forms has connections with a broad spectrum of mathematical areas including number theory, geometry, and Ktheory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers uptodate on research and open problems in representation theory of integral quadratic forms, the algebraic theory of finite square class fields, and developments in the theory of Witt groups of triangulated categories. The specialized articles present important developments in both the algebraic and arithmetic theory of quadratic forms, as well as connections to geometry and Ktheory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms. Readership Graduate students and research mathematicians interested in various aspects of the theory of quadratic forms. Table of Contents  R. Aravire and B. Jacob  The Milnor sequence for \(W_q\mathcal{F}(x)\) in characteristic 2 when \(\mathcal{F}\) is perfect
 L. ArenasCarmona  Spinor norm for local skewHermitian forms
 P. Balmer  An introduction to triangular Witt groups and a survey of applications
 W. K. Chan, A. G. Earnest, and B.K. Oh  Regularity properties of positive definite integral quadratic forms
 W. K. Chan and M. I. Icaza  Effective results on representations of quadratic forms
 W. K. Chan and M. Peters  Quaternary quadratic forms and Hilbert modular surfaces
 M. Dickmann and A. Petrovich  Real semigroups and abstract real spectra. I
 M. Gaulter  The role of characteristic vectors in the neighbour lattice process
 L. J. Gerstein  On representation by quadratic \(\mathbb{F}_q[x]\)lattices
 D. W. Hoffmann  Diagonal forms of degree \(p\) in characteristic \(p\)
 D. G. James  Local densities and the representations of an integer by a definite quadratic form
 M. Karoubi  Periodicity of Hermitian Ktheory and Milnor's Kgroups
 N. A. Karpenko  Third proof of second gap in dimensions of quadratic forms from \(I^n\)
 M.H. Kim  Recent developments on universal forms
 W. Kohnen  Special Siegel modular forms and singular series polynomials of quadratic forms
 A. Laghribi  Quasihyperbolicity of totally singular quadratic forms
 D. B. Leep and T. L. Smith  Witt kernels of triquadratic extensions
 D. W. Lewis  Antiautomorphisms of the second kind
 J. Martinet  Reduction modulo 2 and 3 of Euclidean lattices, II
 M. Marshall  The elementary type conjecture in quadratic form theory
 A. Pfister  On Hilbert's theorem about ternary quartics
 R. SchulzePillot  Representation by integral quadratic formsA survey
 R. SchulzePillot and F. Xu  Representations by spinor genera of ternary quadratic forms
 T. Watanabe  A survey and a complement of fundamental Hermite constants
