Lectures related to Analysis of ARV

Probability Convergence

Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Cartesian Product and Induction

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

Probability Theory: Lecture 2

Explores toy models, sigma-algebras, T-valued random variables, measures, and independence in probability theory.

Probability and Statistics

Delves into probability, statistics, paradoxes, and random variables, showcasing their real-world applications and properties.

Probability and Statistics

Introduces key concepts in probability and statistics, illustrating their application through various examples and emphasizing the importance of mathematical language in understanding the universe.

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

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.

Holomorphic Functions: Taylor Series Expansion

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

Random Variables: Expectation and Independence

Explores random variables, expectation, and independence in probability theory.

Thermodynamic formalism for coarse expanding dynamical systems

Explores thermodynamic formalism for weakly coarse expanding dynamical systems, covering equilibrium states, visual metrics, and symbolic coding.

Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Intrinsic Geometry of Regular Surfaces

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

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.

Generalization Error

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

Linear Algebra: Applications and Definitions

Covers the definition of applications, image of elements, and direct and reciprocal images.

Infinite Coin Tosses: Independence

Explores independence in infinite coin tosses, covering sets, shifts, and T-invariance.

Random Variables and Covariance Log in to Mediaspace to watch this video

Covers random variables, variances, and covariance, as well as the probability in random graphs.

Metric Spaces: Topology and Continuity Log in to Mediaspace to watch this video

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Heterogeneous Catalysis: Adsorption & Kinetics Log in to Mediaspace to watch this video

Explores adsorption mechanisms, elementary kinetics, active sites, and transport effects in heterogeneous catalysis.