Core Courses
The BMS Core Course sequences in RTA 5 cover the fundamental concepts, results, and methods in discrete geometry, understood in a broad sense. Adjacent fields with mutual cross-fertilization include combinatorics, algebraic and differential geometry, topology, functional analysis, and optimization. Application areas include computational biology, physics, economics, and more.
Classical Geometries
This course serves as an introduction to discrete differential geometry. Key topics include projective geometry, spherical and hyperbolic geometry, Möbius geometry, Lie sphere geometry.
This course is a second course in discrete differential geometry. Key topics include discrete surfaces and polyhedral complexes, discretizations of mean and Gauss curvature, Delaunay triangulations, subdivision surfaces, discrete Hodge theory, geometry processing.
Discrete Geometry I + II
These two courses cover the foundations of polytope theory, making the connection to linear optimization. Key topics include Minkowski-Weyl-Theorem, McMullen's Uppper Bound Theorem, Dehn-Sommerville equations, computing convex hulls, Voronoi digrams, regular subdivisions of point configurations.
Spectrum of Advanced Courses
Lattice polytopes, toric geometry, tropical geometry, combinatorial algebraic geometry, solving systems of polynomial equations, high dimensional convex geometry, geometry of numbers, isoperimetric problems, combinatorial topology.
