Lectures related to Ruelle resonances for geodesic flow on noncompact manifolds

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

Explores uncertainty quantification using Quasi Monte Carlo methods and discrepancy measures for integral approximation and volume estimation.

Covers conformal blocks, Young diagrams, and their significance in weight states.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Explores historical mathematical proofs, decision problems, deductive systems, probabilistic and quantum proofs, and interactive proof systems.

Explores the proof of properties related to the delta function in mathematical analysis.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

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

Covers Dognion's Theorem, explaining the proof of infeasible Integer Programming problems.

Explores implicit schemes in numerical analysis, emphasizing stability and convergence properties in solving differential equations.

Explores geodesics in the Wasserstein space, emphasizing constant speed geodesics and their properties.

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Explores the conditions for injectivity in mathematical functions, with detailed examples and proofs.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Covers the (log n) approximation algorithm for the sparsest cut problem, presenting the mathematical theorems and proofs.

Explores the concept of universal coating through detailed proofs and examples, emphasizing uniqueness and significance.

Emphasizes mathematical rigor, clear communication, and exercise organization in teaching methods.

Covers open balls, lemma statements, and proof techniques in embedding into l_inf.

Covers the resolution of boundary problems in 1D, focusing on mathematical concepts and equations.

Covers the duality principle in linear algebra and its implications in mathematics.