Title: Tropical obstructions to stable rationality
Abstract: It is an old and thorny problem in algebraic geometry to determine which projective hypersurfaces are rational, or, more generally, stably rational, meaning that they become rational when we take the product with a projective space of sufficiently large dimension. I will explain how one can use degeneration techniques and tropical methods to find new classes of non-stably rational hypersurfaces and complete intersections. This talk is based on joint work with John Christian Ottem.