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Multidimensional Residues and Tropical Geometry
June 17, 2021 18:00–19:00, Plenary session, Sochi
 


Higher convexity of tropical objects

F. Sottile

Texas A&M University

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Abstract: Gromov generalized the notion of convexity for open subsets of $R^n$ 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.

Language: English

Website: https://us02web.zoom.us/j/2162766238?pwd=TTBraGwvQ3Z3dWVpK3RCSFNMcWNNZz09

* ID: 216 276 6238, password: residue

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