Dec 2 – 3, 2020
Le Bois-Marie
Europe/Paris timezone

On a Tropical Version of the Jacobian Conjecture

Dec 3, 2020, 11:00 AM
50m

Speaker

Dimitri Grigoryev (CNRS Painlevé Lab, Univ. Lille)

Description

We prove that, for a tropical rational map if for any point the convex hull of Jacobian matrices at smooth points in a neighborhood of the point does not contain singular matrices then the map is an isomorphism. We also show that a tropical polynomial map on the plane is an isomorphism if all the Jacobians have the same sign (positive or negative). In addition, for a tropical rational map we prove that if the Jacobians have the same sign and if its preimage is a singleton at least at one regular point then the map is an isomorphism. This is a joint work with Danylo Radchenko, ETH (Zürich).

Presentation materials