Lectures related to Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

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

Explores Lagrange interpolation, emphasizing uniqueness and simplicity in reconstructing functions from limited values.

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

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

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

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

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

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

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

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

Covers the application of the Weingarten map on regular surfaces and the shape operator.

Covers the theory and applications of bilinear forms in various mathematical contexts.

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

Covers the definition of differential equations and their relation to functions and derivatives.