Lectures related to Minkowski's Theorems: Lattices and Volumes

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Explores the consequences of double integrals, including compact sets and continuity.

Delves into lattice theory, emphasizing Minkowski's theorems and their implications on lattice structures.

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

Covers Jordan-measurable sets, Riemann-integrability, and function continuity on compact sets.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Explores convex sets, Minkowski-Weyl theorem, and Separation theorem in convex analysis.

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Explores compact sets, extreme values, and function theorems on bounded sets.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores the Lebesgue integral, where functions self-select partitions, leading to measurable sets and non-measurable complexities.

Covers the concept of outer measure and properties of measurable sets.

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

Covers the properties of the Lebesgue measure and its existence.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Covers extreme values of continuous functions on compact sets and differentiability.

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Explores the construction of measures, emphasizing positive functionals and their connection to the Riesz-Kakutani Theorem.