Lectures related to Hamiltonian dynamics on convex polytopes

Explores the complexity of convex hulls and the concept of vertices within them.

Optimal Transport: Regularity and Brenier's Theorem

Explores optimal transport regularity and Brenier's theorem, discussing continuity and convexity concepts.

Optimization Techniques: Gradient Descent and Convex Functions

Provides an overview of optimization techniques, focusing on gradient descent and properties of convex functions in machine learning.

Sparsest Cut: ARV Theorem

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.

Composition of Applications in Mathematics

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

Central Limit Theorem

Covers the Central Limit Theorem and its application to random variables, proving convergence to a normal distribution.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.