Event time:
Thursday, March 3, 2016 - 11:30am to 12:30pm
Location:
431 DL
Speaker:
Frank Sottile
Speaker affiliation:
Texas AM University
Event description:
Gromov generalized the notion of convexity for open subsets of $\mathbf{R}^n$ with hypersurface 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.