Lectures related to Spectral Expansion: Eisenstein Series

Canonical Embedding: Fields and Lattices

Explores canonical embedding of #-fields, lattices, and finiteness of class groups.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Goldstone Bosons: Higgs Mechanism

Explores Goldstone bosons and the Higgs mechanism, revealing how spontaneous symmetry breaking generates mass for gauge bosons.

Eigenstate Thermalization Hypothesis

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

Quantum Field Theory: Fermions and Grassmann Numbers

Explores quantum field theory, focusing on fermions and Grassmann numbers in the path integral formalism.

Sturm-Liouville Problem: Homogeneous Boundary Conditions Essential Role

Explores the Sturm-Liouville eigenvalue problem, emphasizing the essential role of boundary conditions in ensuring self-adjointness and forming an orthogonal basis.