Lectures related to Adelic Number Theory

Poincaré Irreps 2: Little Group and Induced Representation

Explores Poincaré irreducible representations, Little Group, and induced representation in the context of momentum eigenstates.

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Lie Algebras and Representations

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Group Algebra: Maschke's Theorem

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Complete Reducibility of Complex Representations

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Molecular Vibrations & Normal Modes

Explores molecular vibrations, normal modes, IR & Raman activity, and symmetry analysis.

Lie Groups and Lorentz Transformations

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

Adelic Topology: Properties and Approximation

Explores adelic topology, lattice representation, and strong approximation properties.

Group Theory: Reducible and Irreducible Representations

Explores group theory in quantum physics, emphasizing reducible and irreducible representations, conservation laws, and group properties.

Kirillov Paradigm for Heisenberg Group

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Machine Learning at the Atomic Scale

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

Spinorial Representations of Lorentz Group

Explores spinorial representations of the Lorentz group and the transformation of fields under Lorentz, emphasizing a constructive approach towards spinors.

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Adelic Number Theory

Explores adelic number theory, emphasizing lattices, modules, linear combinations, and Z-linear properties.

Molecular Orbital Theory

Covers the concept of eigenfunctions of H as bases for irreducible representations and integrals.

Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Quantum Circuits: Models and Approximations

Explores quantum circuit modeling, approximations, unitary matrices, and measurement operations.

Symmetries in Quantum Field Theory

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