Lectures related to Diophantine Approximation: Minbowski's Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Explores the Second Separation Theorem for closed convex sets and the concept of supporting hyperplanes.

Explores Minkowski's theorems on lattices, volumes, and set comparisons.

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Introduces Cartesian product and induction for proofs using integers and sets.

Covers the KKT conditions and convex optimization, discussing constraint qualifications and tangent cones of convex sets.

Covers the concept of convex functions and their applications in optimization problems.

Explores Gaussian corelation inequality, Anderson's theorem, and log-concavity in probability theory.

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Covers weak derivatives, their properties, and applications in functional analysis.

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores convex functions, global minima, and their relationship with differentiability.

Explores unconstrained optimization theory, covering global and local minima, convexity, and gradient concepts.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Explores convex sets, their properties, and applications in optimization.