Leírás
In the last 25 years, limit theories for graphs and other combinatorial structures have been worked out, allowing us to approximate very large finite structures by smoother, continuous structures. For graphs, the limit objects are quite well described, and various associated structures (spanning trees, matchings, automorphism groups, spectra), and their convergence to the corresponding structure in the limit, are quite well understood. The matroid of a graph is another associated structure, which carries a lot of information about the graph (spanning trees, connectivity, planarity, etc.). In this talk I sketch some recent results on how to define convergence of a sequence of matroids (or more generally submodular set functions on finite sets), and how to construct an appropriate limit object. This is joint work with Kristóf Bérczi, Márton Borbényi, and László Márton Tóth.