Lectures related to Integral Representations: Quadratic Lattices and Hasse Principle

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.

Discusses quadratic forms, matrix diagonalization, and their applications in optimization problems.

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

Explores the definition and properties of Hermitian forms in complex vector spaces.

Covers the concept of orthogonal groups in finite-dimensional vector spaces and their special properties.

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

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

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

Covers elliptical distributions, including properties, applications, and risk management implications.

Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.

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