Lectures related to Distribution Interpolation Spaces

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

Advanced Analysis 2: Continuity and Limits

Delves into advanced analysis topics, emphasizing continuity, limits, and uniform continuity.

Calculus of Variations: Principles and Applications

Explores the principles and applications of calculus of variations, focusing on uniform boundedness and equi-integrability of Carathéodory integrands.

Uniform Integrability and Convergence

Explores uniform integrability, convergence theorems, and the importance of bounded sequences in understanding the convergence of random variables.

Convergence of Random Variables

Explores the convergence of random variables, the law of large numbers, and the distribution of failure time.

Bolzano-Bastra-Sterl: Applications and Uniform Continuity

Explores the Bolzano-Bastra-Sterl theorem and uniform continuity in sequences.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Distribution to Spaces: Interpolation and Continuity

Covers weak derivatives, interpolation spaces, and continuity in function spaces.

Differential Equations: Solutions and Periodicity

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

Quadratic Penalty Method: Finer Analysis

Covers the quadratic penalty method and augmented Lagrangian, including the setup and convergence of sequences.

Intermediate Value Theorem

Covers the Intermediate Value Theorem, uniform continuity, Lipschitz functions, and the properties of continuous functions.

Sparsest Cut: Bourgain's Theorem

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Diffusion Models

Explores diffusion models, focusing on generating samples from a distribution and the importance of denoising in the process.

Existence of Solutions for Poisson-Dirichlet Problem

Covers the existence of solutions for the Poisson-Dirichlet problem, focusing on showing that certain conditions hold for locally bounded and Hölder continuous functions.

Real Functions: Continuity Extension

Discusses extending a function uniformly and its continuity properties in real functions.

Vector Spaces and Convergence

Covers vector spaces, compact sets, convergence, continuity, and uniqueness theorems.

Finite Element Method: Weak Solutions

Covers weak solutions in the finite element method, emphasizing continuity and the Cauchy-Schwarz inequality.

Sequence Convergence: Definitions and Properties

Covers definitions and properties of sequence convergence, including limits, uniqueness, and the two gendarmes theorem.

Limit of a Sequence

Explores the limit of a sequence and its convergence properties, including boundedness and monotonicity.