Lectures related to Residue Fields and Quadratic Forms

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Explores integral representations, quadratic lattices, and the Hasse Principle.

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Covers non-degenerate integral quadratic lattices and adèles, including their properties and definitions.

Explores quadratic forms, symmetric bilinear forms, and their properties.

Explores examples of algebraic quotients using invariance maps and discriminant.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Explores symmetric matrices, quadratic forms, and critical points in functions of two variables.

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Explores the precision of finite element models and higher order asymptotic estimates.

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Explores precision of higher order finite element models and applications of quadratic finite elements in elastodynamics.

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Explores the theory of Hermitian spaces and their applications in quadratic forms and codimension 1 spaces.

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Explores ramified extensions and Eisenstein polynomials, showcasing their applications in mathematical contexts.

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.