Lectures related to Integral Quadratic Lattices: Properties and Adeles

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

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

Discusses Fermat's equation and Gaussian integers' properties.

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Explores integral representations, quadratic lattices, and the Hasse Principle.

Explores residue fields, quadratic forms, discriminants, and Dedekind recipes in algebraic number theory.

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Explores quadratic forms, symmetric bilinear forms, and their properties.

Explores the properties of commutative rings and integral domains in algebra.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Explores examples of algebraic quotients using invariance maps and discriminant.

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Covers the ring of polynomials, focusing on coefficients and multiplication.

Covers optimization methods without constraints, including gradient and line search in the quadratic case.

Explores the joint equidistribution of CM points for cubic fields, emphasizing periodic orbits and quadratic algebraic forms.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.