Lectures related to Invariant theory

Eisenstein Series and Spectral Decomposition

Covers Eisenstein series properties and spectral decomposition of functions.

Explores symmetries in quantum field theory, focusing on transformation rules and Casimir operators.

Covers projectors on invariant subspaces in quantum physics and their applications.

Explores a criterion for computing quotients in algebraic geometry, emphasizing the importance of normality and g-invariant morphisms.

Remarks about the Quotient

Explores the concept of the quotient in linearly reductive groups and varieties, discussing irreducibility, normality, and integral properties.

Algebraic Quotients

Covers the concept of algebraic quotients in the context of a-variety.

Representation Theory: Actions and Invariants

Covers the representation theory of groups, focusing on actions and invariants.

Geometric Projections: Historical Perspectives and Applications

Explores the evolution of projective geometry and its applications in architectural representation.

Understanding Vacuum Energy in Inflation

Explores vacuum energy during inflation and the dynamics of scalar and vector fields, emphasizing the importance of seeking clarification and providing details about upcoming exams.

Machine Learning at the Atomic Scale

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Lemma of Schur: Group Repetition Theory

Explores irreducible and reducible representations in group repetition theory and the lemma of Schur in quantum physics.

Matrix Representations of Linear Applications

Explores matrix representations of linear applications, including change of basis and invariants.

Representations of SU(2): Symmetries and Transformations

Covers the representations of SU(2) and their transformations in quantum mechanics.

Periodic Orbits of Hamiltonian Systems

Covers the theory of periodic orbits of Hamiltonian systems and the Conley-Zehnder index.

Further Directions: Algebraic Groups

Explores various directions for studying algebraic groups and offers references for further exploration.

Tensor Spaces and Unitary Representations

Explores tensor spaces, unitary representations, and prime factorization in mathematical presentations.

Linear Algebra: Decomposition Theorems

Covers the proof of primary decomposition theorem for endomorphisms of finite-dimensional vector spaces.

Eigenvalues and Eigenvectors

Covers the concept of eigenvalues and eigenvectors in linear algebra, focusing on the properties of endomorphisms.

Jordan Normal Form: Part 1

Covers the Jordan normal form and the decomposition of vector spaces by an endomorphism.

Transformation Laws: Diagonalization of Symmetric Tensors

Discusses tensor transformations and diagonalization of symmetric tensors, focusing on stress analysis and the significance of principal stresses.