Lectures related to Equidistribution of CM Points

Topology of Adeles

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

Quadratic Forms and Symmetric Bilinear Forms

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

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Finite Element Method: Higher Order Models

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

Cauchy Equations and Integral Decomposition

Covers the application of Cauchy equations and integral decomposition, addressing questions related to holomorphic functions and Jacobian matrices.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

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

Integral Quadratic Lattices: Properties and Adeles

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

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.

Local Global Duality

Explores local-global duality in lattices and joint equidistribution of CM points.

Finite Element Method: Quadratic Elements

Explores the precision of finite element models and higher order asymptotic estimates.

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.

Elliptical Distributions: Properties and Applications

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

Algebra: Fundamental Theorem

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Classification of Quadratic Forms

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

Quadratic Forms and Symmetries

Explores quadratic forms, symmetries, representations, and orthogonal sums in mathematics.

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.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Algebraic Structures: Classes and Cyclic Groups

Explores algebraic structures, classes of examples, and properties of cyclic groups.