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Automatic Vectorization: Principles and Applications

Covers the potential and limits of automatic vectorization techniques for digitizing objects from scanned documents or images.

Projective Geometry: Anharmonic Cross Ratio and Conics

Explores anharmonic cross ratio, projective geometry birth, and practical applications.

Hamiltonian dynamics on convex polytopes

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

Projective Plane Curves

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Discrete variables: Geometric properties

Covers geometric properties of discrete variables in GIS, including location, size, and shape.

Divergence Theorem: Green Identities in R²

Explores the divergence theorem and corollaries related to Green identities in the plane, demonstrating their application through examples.

Plane Curves: Singular Points and Multiplicities

Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Catalan Numbers: Theory and Applications

Explores Catalan numbers in cutting polygons, parenthesis structures, and Dyck paths.

Cauchy Integral Formula

Covers the Cauchy Integral Formula, Morera's Theorem, Liouville's Theorem, and the Fundamental Theorem of Algebra.

Topologie: Attachment Applications

Covers exercises on attaching 1-cells to intervals in topology.