Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Connections: motivation and definition Log in to Mediaspace to watch this video

Explores the definition of connections for smooth vector fields on manifolds.

Untitled Log in to Mediaspace to watch this video

Riemannian connections Log in to Mediaspace to watch this video

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Local Rings and Residues Log in to Mediaspace to watch this video

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Graph Coloring: Theory and Applications Log in to Mediaspace to watch this video

Covers the theory and applications of graph coloring, focusing on disassortative stochastic block models and planted coloring.

Lax-Milgram: Variational Problems and Riesz's Theorem Log in to Mediaspace to watch this video

Explores the Lax-Milgram theorem, variational problems, and Riesz's representation theorem in linear elliptic problems.

Curvature and Osculating Circle Log in to Mediaspace to watch this video

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Likelihood Ratio Tests: Optimality and Applications Log in to Mediaspace to watch this video

Explores the theory and applications of likelihood ratio tests in statistical hypothesis testing.

Differential Geometry: Parametric Curves & Surfaces Log in to Mediaspace to watch this video

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

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.

Application Reciproque and Composition of Applications Log in to Mediaspace to watch this video

Explores the relationships between functions and sets, focusing on composite functions properties.

Shape from Texture Log in to Mediaspace to watch this video

Explores recovering surface orientation from image texture under different projections and the use of deep learning for normal prediction.

Taylor Polynomials: Approximating Functions in Multiple Variables Log in to Mediaspace to watch this video

Covers Taylor polynomials and their role in approximating functions in multiple variables.

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