Lectures related to Finitely generated group

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Isotypic Decomposition: Finitely Generated C-Algebras

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

McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.

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.

Effective Field Theory: Universal Description at Low Energies

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

Orbit-Stabilizer Theorem: Conjugacy Classes and Direct Products

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Introduction, Ch V: Sylow Subgroups

Explores the study of finite groups through subgroup analysis, focusing on Sylow subgroups.

Endomorphisms and automorphisms of totally disconnected locally compact groups II

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

Rings and Modules: Lecture 1

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Surface of Revolution

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

Self-similar groups II

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

Module Theory: Noetherian Modules

Introduces Noetherian modules and explores simple modules and composition series.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Existence of Sylow Subgroups

Explores the proof of the existence of Sylow subgroups in group theory.

Properties of Sylow Subgroups: Group Theory

Explores the beautiful properties of the p-Sylow subgroups of a finite group.

Conjugation in Groups

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

Finite Elements Transformation

Covers the transformation of finite elements into deformed elements and the evaluation of the Jacobian matrix.

Finite Abelian Groups: Classification Theorem

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Classification of Finite Abelian Groups

Covers the classification theorem for finite abelian groups and introduces rings, including zero divisors and domains.