## Colloquium

•  Frank Sottile, Texas A&M University
•  Higher convexity for complements of tropical objects
•  10/17/2019
•  4:10 PM - 5:00 PM
•  C304 Wells Hall

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.

## Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science