Lectures related to Symplectic Groups

Bilinear Forms: Theory and Applications

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

Differential Forms on Manifolds

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

Linear Algebra: Multilinear Forms

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

The Torus and Linear Groups

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Linear Algebra: Multilinear Forms

Explores multilinear forms in linear algebra, emphasizing their properties and applications.

Linear algebraic groups

Covers linear algebraic groups, including special sets and matrix examples.

Conformity and Compliancy in Geometry

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

Weingarten Application of Regular Surfaces

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

Linear Algebra: Elementary Row Operations

Covers elementary row operations, equivalent matrices, invertibility, and bases in linear algebra.

Pseudo-Euclidean Spaces: Isometries and Bases

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

Quadratic Forms and Symmetric Bilinear Forms

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

Diagonalizable Groups

Explores the concept of diagonalizable groups and their properties in linear algebraic groups.

Linear Projective Groups

Explores linear projective groups, quaternions, subgroup generation, and normality.

Linear Algebra: Quadratic Forms and Matrix Diagonalization

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

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Lax-Milgram: Variational Problems and Riesz's Theorem

Explores the Lax-Milgram theorem, variational problems, and Riesz's representation theorem in linear elliptic problems.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.