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 K-theory. This volume contains survey and research articles covering the range of connections among these topics. The survey articles bring readers up-to-date 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 K-theory. The volume is suitable for graduate students and research mathematicians interested in various aspects of the theory of quadratic forms.

Table of Contents:
The Milnor sequence for $W_q\mathcal{F}(x)$ in characteristic 2 when $\mathcal{F}$ is perfect by R. Aravire and B. Jacob Spinor norm for local skew-Hermitian forms by L. Arenas-Carmona An introduction to triangular Witt groups and a survey of applications by P. Balmer Regularity properties of positive definite integral quadratic forms by W. K. Chan, A. G. Earnest, and B.-K. Oh Effective results on representations of quadratic forms by W. K. Chan and M. I. Icaza Quaternary quadratic forms and Hilbert modular surfaces by W. K. Chan and M. Peters Real semigroups and abstract real spectra. I by M. Dickmann and A. Petrovich The role of characteristic vectors in the neighbour lattice process by M. Gaulter On representation by quadratic $\mathbb{F}_q[x]$-lattices by L. J. Gerstein Diagonal forms of degree $p$ in characteristic $p$ by D. W. Hoffmann Local densities and the representations of an integer by a definite quadratic form by D. G. James Periodicity of Hermitian K-theory and Milnor's K-groups by M. Karoubi Third proof of second gap in dimensions of quadratic forms from $I^n$ by N. A. Karpenko Recent developments on universal forms by M.-H. Kim Special Siegel modular forms and singular series polynomials of quadratic forms by W. Kohnen Quasi-hyperbolicity of totally singular quadratic forms by A. Laghribi Witt kernels of triquadratic extensions by D. B. Leep and T. L. Smith Anti-automorphisms of the second kind by D. W. Lewis Reduction modulo 2 and 3 of Euclidean lattices, II by J. Martinet The elementary type conjecture in quadratic form theory by M. Marshall On Hilbert's theorem about ternary quartics by A. Pfister Representation by integral quadratic forms-A survey by R. Schulze-Pillot Representations by spinor genera of ternary quadratic forms by R. Schulze-Pillot and F. Xu A survey and a complement of fundamental Hermite constants by T. Watanabe.