Residue Fields and Quadratic Forms

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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.