Lectures related to Index of a subgroup

Delves into the symmetries of regular polygons, including the dihedral group and left cosets in a finite group.

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

Group Theory: Properties and Examples

Introduces the concept of a group and its properties through illustrative examples.

Fault tolerance: Stabilizer Subgroup

Explores fault tolerance, error propagation, and the Gottesman-Kill Theorem in stabilizer subgroups.

Homomorphisms: Birational Maps and Affine Varieties

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Lagrange's Theorem: Applications and Homomorphisms

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Points fixes et orbites

Covers fixed points, orbits, and stabilizer subgroups in group actions.

Definition: Understanding Group Structures

Explores the philosophy of understanding a group through its subgroups' structure, focusing on finite groups.

Algebra: Practice Exam Solutions

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

McKay Graphs of Finite Subgroups of SU(2)

Explores McKay graphs for finite subgroups of SU(2) and the corresponding Coxeter graphs.

Weyl Characters and Borcherds Products

Explores Weyl characters, Macdonald's identities, and Borcherds products in Euclidean space.

Geometric McKay correspondence: Du Val singularities and Dynkin diagrams

Explores the derivation of Dynkin diagrams from Du Val singularities.

Mathematical Parenthesis on Groups and Lagrange Theorem

Explores cosets in commutative groups, Lagrange theorem, and integer factorization.

Group Theory: Quotients of Group

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

RSA Cryptosystem: Encryption and Decryption Process

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

Euclidean Isometries: Properties and Applications

Explores the properties and applications of Euclidean isometries in R^2.

Covers self-similar groups and automorphisms of rooted trees, exploring residually finite groups and congruence subgroups.