Generalizations and Applications of the Lovász Theta Number

The theta number of Lovász of a graph, originally invented to determine the Shannon capacity of the pentagon, has been a source of inspiration for everybody working in the area of semidefinite programming (linear optimization over the convex cone of positive semidefinite matrices). By Lovász' sandwich theorem the theta number is sandwiched between the independence number of the graph and the chromatic number of the complementary graph. In this talk I want to discuss generalizations (to hypergraphs), strengthenings, and applications (in coding theory and geometry) of the Lovász theta number. In concrete applications harmonic analysis will be key to perform explicit computations.