Lectures related to Computer-assisted proof

Covers the rigorous proof of differential equations, emphasizing accuracy and precision.

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

Explores formal verification using the LISA proof assistant and the OCBSL Equivalence Checker.

Covers the LISA proof assistant's codebase organization, kernel package, FOL formalization, and proof package.

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

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 Newtonian potential in bounded domains, discussing its conditions and properties.

Covers the demonstration of a theorem regarding the minimum and maximum of a function.

Explores the Cauchy-Schwarz inequality in integrals and functions, offering a comprehensive understanding of its applications.

Covers the definition of an inductive data type in Coq and how to build proofs interactively using tactics.

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