Lectures related to Probabilistic Takens delay embedding theorem

A Conjecture of Erdös: Proof by Moreira, Richter and Robertson

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Probability Theory: Integration and Convergence

Covers topics in probability theory, focusing on uniform integrability and convergence theorems.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

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Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Theorems in Analysis

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Topology of Riemann Surfaces

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

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Analysis IV: Convergence Theorems and Integrable Functions

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Analysis IV: Convolution and Hilbert Structure

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.