Current Developments in Mathematics
Tropical geometry of matroids
Pages: 1 – 46
Lecture notes for Current Developments in Mathematics 2016, based on joint work with Karim Adiprasito and Eric Katz. We give a gentle introduction to the main result of “Hodge theory for combinatorial geometries” [arXiv:1511.02888], the Hodge–Riemann relations for matroids, and provide a detailed description of the geometry behind from a tropical point of view.