Lectures related to Equidistribution of CM Points

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

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Topology of Adeles

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

Linear Quadratic (LQ) Optimal Control: Proof of Theorem

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

Quadratic Forms and Symmetric Bilinear Forms

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

Atomic Structure: Quantum Mechanics

Covers atomic theory, Schrödinger equation, quantum numbers, electron configurations, and periodic properties of elements.

Hermitian Spaces: Theory and Applications

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

Probability Theory: Lecture 2

Explores toy models, sigma-algebras, T-valued random variables, measures, and independence in probability theory.

Pseudo-Euclidean Spaces: Isometries and Bases

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

Differential Forms Integration

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

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Periodic Orbits of Hamiltonian Systems

Explores periodic orbits in Hamiltonian systems and their stability under various conditions.

Symmetric Matrices and Quadratic Forms

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

Symmetric Matrices and Quadratic Forms

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

Classification of Quadratic Forms

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

Integral Quadratic Lattices: Properties and Adeles

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Quadratic Lattices: Properties and Equidistribution

Covers non-degenerate quadratic lattices, local representability, equidistribution, and the Siegel theorem.

Finite Element Method: Higher Order Models

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