Lectures related to Quadratic Forms and Symmetries

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

Explores symmetric matrices, diagonalization, and quadratic forms properties.

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

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

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

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

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

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

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

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

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

Explores examples of algebraic quotients using invariance maps and discriminant.

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

Introduces the quadratic linking degree in motivic knot theory, covering knot theory basics, algebraic geometry, and intersection theory.

Explores Gaussian vectors, moment generating functions, independence, density functions, affine transformations, and quadratic forms.

Explains the Principal Axes Theorem for symmetric matrices and quadratic forms, showing the existence of orthogonal matrices for diagonalization.

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

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

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

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.