Lectures related to Algebraic Structures: Classes and Cyclic Groups

Integration on H_pxH and Arithmetic

Explores integration on H_pxH and arithmetic properties, including norms, structures, and polynomial factorization.

Equidistribution of CM Points

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Algebraic Structures of Morphism Spaces

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Topology: Free Groups and Their Properties

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Decomposition of Group Algebras

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

Algebraic Decomposition: Understanding Simple Algebraic Structures

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Exponential Maps: Properties and Applications in Lie Groups

Covers the properties of the exponential map in Lie groups and their algebras, including smoothness and the relationship between subgroups and algebras.

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

DVR and Irreducible Plane Curves

Explores Discrete Valuation Rings and their role in irreducible plane curves.

Polynomial Rings and Irreducibility Criteria

Covers polynomial rings, irreducibility criteria, and algebraic structures in fields.

Direct Sum of Abelian Groups

Explores the direct sum of abelian groups, emphasizing bijections and uniqueness.

Algebraic Structures: Groups and Rings

Introduces algebraic structures essential for understanding mathematical objects used in science and engineering.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Algebraic Structures: Fields and Vectorial Spaces

Covers prime numbers, vectors, 3D geometry, crystallography, and algebraic structures in materials science.

Ring Homomorphisms and Ideals

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Algebra: Fundamental Theorem

Covers a general introduction and discusses algebra, emphasizing the importance of unique factorization in algebraic structures.

Regularity and Noetherian Local Rings

Covers the concepts of regularity and Noetherian local rings in algebraic structures.

Rings and Fields

Explores rings, fields, ideals, and their properties in algebraic structures.

Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.