Lectures related to Proofs and Refutations

Introduces the Cauchy-Lipschitz theorem and demonstrates uniqueness of global solutions.

Explores formally secure compilation, emphasizing the importance of mathematical proofs and compartmentalization in ensuring component security.

Explores optimal transport theory, transport maps, entropy, and their practical implications in mathematical optimization.

Covers solutions to the 2018 exam, focusing on bounded functions and distinct solutions.

Explores Projected Gradient Descent and related optimization methods using Bregman Divergence.

Covers the organization of the Analyse II course for 2021, including webinars, exercises, and the final exam.

Explores the Supremum Theorem, its properties, proofs, and exercises.

Explores the definition and properties of traces in functional analysis, emphasizing uniqueness and linear operators.

Demonstrates how to use a specific function to prove Rolle's Theorem.

Covers integration on H_pxH and arithmetic topics, focusing on the Hensel Lemma and the process of finding R and S such that R.S-P=0.

Explores quasilocality in statistical mechanics and the existence conditions of Gibbs measures.

Explores exploration bias and generalization bound in KL divergences, emphasizing mathematical proofs and implications.

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

Covers control structures, quadratic equation algorithm design, and correctness verification.

Covers 3-dimensional Anosov flows, exponential mixing, transfer operators, and equilibrium measures.

Explores Maxwell's equations in vacuum, photon scanning near-field optical microscope, light confinement, and experimental proof of light effects.

Covers absolute value, subtraction in integers, and comparisons between integers.

Explores continuity and derivability in heat analysis, emphasizing uniform convergence and mathematical proofs.

Explores theorem proving in first-order logic and the saturation-based approach, highlighting the Vampire theorem prover.

Explains the induction principle and proofs by induction with examples like 1 + 3 + 5 + ... + (2n-1) = n².