Lectures related to Generating set of a group

Explores effective field theory, emphasizing its application to the standard model and the hierarchy problem.

Covers the Postnikov tower, homotopy fibers, suspension, and the James construction.

Covers the concept of the free product in group theory and how to determine monomorphisms and homomorphisms.

Delves into homotopy identification, pushout diagrams, colimits, and group fundamental calculations.

Explores isotypic decomposition in finitely generated C-algebras and its implications, including G-stable ideals and linear projections.

Explores self-similar groups acting on rooted trees and their properties.

Covers subsets in group theory and Lagrange's theorem with examples.

Explores the motivations for studying actions through the universal action of bijections.

Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.

Formalizes the construction of orbits and fixed points in group actions, defining morphisms and verifying naturalness.

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

Introduces Noetherian modules and explores simple modules and composition series.

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Explains the parametric equations of surfaces of revolution generated by curves in space.

Explores vector spaces, bases, and dimensions, including properties and proofs.

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

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Explores integer factorization using the quadratic sieve method and the challenges of working with algebraic number fields.