|Date: Tuesday, November 10, 2015
Title: Higher convexity for complements of tropical objects
Abstract: Gromov generalized the notion of convexity for open subsets of R^n with hypesurface boundary, defining k-convexity, or higher convexity and Henriques applied the same notion to complements of amoebas. He conjectured that the complement of an amoeba of a variety of codimension k+1 is k-convex. I will discuss work with Mounir Nisse in which we study the higher convexity of complements of coamoebas and of tropical varieties, proving Henriques' conjecture for coamoebas and establishing a form of Henriques' conjecture for tropical varieties in some cases.
Speaker: Frank Sottile
Institution: Texas A & M University