Lectures related to Cantor set

Computing leading eigenvalues of the transfer operator

Explores computing the leading eigenvalue of a transfer operator beyond periodic points, focusing on mathematical settings, spectral radius estimation, and the Zaremba Conjecture.

Fractal Uncertainty Principle and Spectral Gaps

Delves into the Fractal Uncertainty Principle for the Fourier transform and spectral gaps, including specialized cases for Cantor sets.

Fractal Uncertainty Principle and Spectral Gaps

Explores transfer operators, Patterson-Sullivan measure, FUP, spectral gaps, and resonances in Schottky groups.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Lebesgue Integration: Cantor Set

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Interior Points and Convergence

Explains interior points, convergence of sequences, and the dense property in real numbers.

Adelic Topology: Properties and Approximation

Explores adelic topology, lattice representation, and strong approximation properties.

Hausdorff Dimension and Brownian Motion

Explores the Hausdorff dimension of Brownian motion zeros, demonstrating a dimension of 1/2 with certainty.

Analysis IV: Measurable Sets and Functions

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Nonlinear Dynamics: Chaos and Complex Systems

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Change of Variable Formula: Devil's Staircase

Explores a change of variable formula and the intriguing Devil's Staircase.

Selected Topics in Mathematics

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

Homomorphisms: Birational Maps and Affine Varieties

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Fractal Dimension: Understanding Complex Geometric Structures

Explores fractal dimension, calculating values analytically and providing practical examples in computer graphics.

Functional Analysis: Banach and Hilbert Spaces

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.

Interior Points and Closure in Real Analysis

Explores interior points, closures, and set properties in real analysis.