Lectures related to Integer Programming: John's Theorem

Explores transference bounds, ellipsoids, and determining the shortest vector.

Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.

Convex Optimization: Introduction and Sets

Covers the fundamentals of convex optimization, including mathematical problems, minimizers, and solution concepts, with an emphasis on efficient methods and practical applications.

Geodesic Convexity: Theory and Applications

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Approximation Algorithms

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

Convex Optimization: Gradient Descent

Explores VC dimension, gradient descent, convex sets, and Lipschitz functions in convex optimization.

Optimal Transport: Rockafellar Theorem

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Small-Angle X-ray Scattering II

Explores Q-regimes, idealized shapes, and scattering curves in small-angle x-ray scattering analysis.

Geodesy Fundamentals: Understanding Earth Reference Systems

Provides an overview of geodesy, focusing on Earth's reference systems and the importance of accurate geodetic data for practical applications.

Hamiltonian dynamics on convex polytopes

Explores Hamiltonian dynamics on convex polytopes, covering symplectic capacities, EHZ capacity, and systolic ratio maximizers.

Geodetic Concepts: Reference Systems and Projections

Covers geodetic concepts, reference systems, and map projections for accurate measurements in engineering projects.

Coordinates and Projection Systems

Explores scales, coordinate systems, map projections, and legal positioning references.

Symmetric Matrices: Eigenvalues and Diagonalization

Covers symmetric matrices, eigenvalues, and diagonalization process for spectral theorem applications.

Coordinate Conversions: Transformations de coordonnées - Conversions

Explores reference systems evolution, coordinate conversions, satellite tracking, and map projections.

Optimal Transport: Convexity and Inequalities

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Variational Problems: Convexity and Coercivity

Explores variational problems, emphasizing convexity and coercivity conditions in functionals with integral side constraints.

Harmonic Forms: Main Theorem

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

Semi-Definite Programming

Covers semi-definite programming and optimization over positive semidefinite cones.