Lectures related to Fractal Uncertainty Principle and Spectral Gaps

Covers the concept of limit at a point and function composition in the context of continuous functions.

Covers the definitions and properties of double integrals over compact regions.

Covers the limit definition of a function and continuity on a set.

Covers advanced topics in analysis, focusing on isolated points, continuity, and level sets.

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Covers the theory and examples of conformal applications, focusing on the concept of conformal mappings and Moebius transformations.

Explores conformal transformations, including holomorphic functions and Moebius transformations.