1. Accueil
  2. EN
  3. Studying at ULB
  4. Find your course
  5. UE
MATH-F429

Géométrie convexe et discrète

academic year
2024-2025
2025-2026

Course teacher(s)

Samuel FIORINI (Coordinator) and Dimitri LEEMANS

ECTS credits

5

Language(s) of instruction

french

Course content

Convexity. Lattices and Minkowski's theorem. Convex independent subsets. Incidence problems. Convex polytopes. Number of faces in arrangements. Lower envelopes. Intersection patters of convex sets. Geometric selection theorems. Transversals and epsilon-nets. Attempts to count k-sets. Two applications of high-dimensional polytopes. Volumes in high dimension. Measure concentration and almost spherical sections. Embedding finite metric spaces into normed spaces.

Objectives (and/or specific learning outcomes)

  • think better in higher dimension;
  • exploit convexity to solve problems arising in mathematics and applications;
  • discover structure in a convex set (discrete or not) and use it;
  • convert between the different representations of a convex set.

Prerequisites and Corequisites

Required and Corequired knowledge and skills

 

Teaching methods and learning activities

Inverted class. Homeworks. Oral exam.

References, bibliography, and recommended reading

  • Matousek, Lectures on Discrete Geometry. Graduate Texts in Mathematics 212, Springer-Verlag New York, 2002.

Course notes

  • Université virtuelle

Other information

Additional information

 

Contacts

Samuel FIORINI (teacher): Samuel.Fiorini@ulb.be

Campus

Plaine

Evaluation

Method(s) of evaluation

  • Other

Other

 

Mark calculation method (including weighting of intermediary marks)

 

Language(s) of evaluation

  • french
  • (if applicable partially in english )

Programmes