Lectures related to Formally Secure Compilation: Ensuring Component Security

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

Covers the basics of formal logic, focusing on logical expressions and mathematical proofs.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 recursion and induction for mathematical proofs through recursive algorithms and functions.