Seminar

Jian He (Symplectic and Contact Geometry and Topology): "Stein manifolds and SFT"


Anders Jensen (Tropical Geometry): "The 4x4 minors of a 5x5 matrix"
Abstract:
In tropical mathematics there are several different notions of rank. Develin, Santos and Sturmfels studied and compared the Kapranov and tropical rank of a matrix. A basic result is that the Kapranov rank of a matrix is greater than or equal to its tropical rank. In this talk we complete the proof that for 5x5 matrices equality holds by presenting a computational proof that the set of all 4x4 minors of a 5x5 matrix of variables is a tropical basis. The computations were carried out by the software Gfan. Moreover, we discuss the practical computational challenges that arise when computing and comparing large tropical varieties and prevarieties with symmetry. In independent work Elena Rubei has given a human readable proof of the rank statement for
5x5 matrices.