November 30, 2021 to December 2, 2021
Le Bois-Marie
Europe/Paris timezone

A Tropical Version of Hilbert Polynomial (remote)

Dec 2, 2021, 2:00 PM
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette


Dimitri Grigoryev (CNRS Painlevé Lab, Univ. Lille)


We define Hilbert function of a semiring ideal of tropical polynomials in n variables. For $n = 1$ we prove that it is the sum of a linear function and a periodic function (for sufficiently large values). The leading coefficient of the linear function equals the tropical entropy of the ideal. For an arbitrary n we discuss a conjecture that the tropical Hilbert function of a radical ideal is a polynomial of degree at most $n − 1$ (for sufficiently large values). For $n = 1$ the conjecture is true, also we have proved it for zero- dimensional ideals and for planar tropical curves.

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