Special Topics in Geometry
- Convex functions, examples and first applications
- Convex functions of several variables
- Three essential operations on convex sets
- Volume and area of (compacts) convex sets
- Volume and Minkowski addition: the Brunn-Minkowski theorem
- Volume and polarity
- Polygons
- Polyhedra: combinatorics
- Regular Euclidean polyhedra
- Regular Euclidean polyhedra
- Isoperimetry for Euclidean polyhedra
- Polytopes (d > 3): combinatorics
- Regular polytopes (d > 3)
- Lattices in the Euclidean plane: classification, density, Fourier analysison lattices
- Packing circles (disks) of the same radius, finite or infinite in number,
in the plane
- Tiling the plane with a group (crystallography)
- Tilings in higher dimensions
- Lattices and packings associated with dimension 3
- Optimal packing of balls in dimension 3
- Lattices in arbitrary dimension
- Packings in arbitrary dimension
- Error correcting codes
- Duality, theta functions, spectra and isospectrality in lattices