Integral Representations: Quadratic Lattices and Hasse Principle

Related lectures (30)

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

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

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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

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

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

Explores residue fields, quadratic forms, discriminants, and Dedekind recipes in algebraic number theory.

Explores examples of algebraic quotients using invariance maps and discriminant.

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