Lectures related to Monodromy: Action and Classes

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers examples of direct and indirect proofs in mathematics.

Covers the concepts of contraposition and contradiction in proofs.

Explores optimal transport in heat equations and metric spaces.

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

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Covers the concept of compression and distance boards.

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

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Introduces Coq, an interactive theorem assistant based on the Curry-Howard isomorphism.

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

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Explores the proof of the Prime Number Theorem and its implications in number theory.

Covers the approximation of functions in Sobolev spaces using smooth functions.

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Covers basic properties of conditional expectation and Jensen's inequality in probability theory.