Integral Quadratic Lattices: Properties and Adeles

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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.