Lectures related to Number Fields: Embeddings and Ideal Classes

Hermite-Minkowski Theorems: Number Fields and Ideal Classes

Explores Hermite-Minkowski theorems in number fields and ideal classes.

Explores the properties and applications of logarithmic embeddings in number fields.

Explores embeddings of number fields, types, signatures, lattices, and determinants.

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

Frobenius Theorems in Number Theory

Explores Frobenius theorems in number theory, ideal class groups, norm properties, and geometry of numbers.

Dynamics on Homogeneous Spaces and Number Theory

Covers dynamical systems on homogeneous spaces and their interactions with number theory.

Ideal Class Group Relations

Covers the relations between the ideal class group and proper fractional ideals.

Dedekind Rings: Factorisation and Ideal Class Group

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

The Discriminant and Ideal Class Group in Mathematics

Explores the discriminant in matrices, ideal class groups, and optimal embeddings in mathematics.

The Class Number Formula: Counting and Lipschitz Principle

Covers the Class Number Formula and a counting problem related to the lattice and Lipschitz principle.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.

Irreducible Factors and Noetherian Rings

Explores irreducible factors, Noetherian rings, ideal stability, and unique factorization in rings.

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Ramification Theory: Residual Fields and Discriminant Ideal

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

The classical Lie algebras

Covers the classical Lie algebras, focusing on calculations and dimensions.

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Cyclotomic Extensions: Norms, Ideals, and Primes

Explores cyclotomic extensions, prime numbers, and ideal norms in number theory.

Chinese Remainder Theorem: Rings and Fields

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Primes in Arithmetic Progression

Explores primes in arithmetic progression, focusing on L-functions, characters, and the divergence of the sum of 1 over p for p congruent to a modulo q.

Congruence Relations in Rings

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.