Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Dima Grigoriev
Affiliation:

CNRS Lille/Bonn
Date:

Mon, 02/12/2019 - 09:30 - 10:30 Combinatorial Nullstellensatz (due to N. Alon) provides conditions in terms of the support of a polynomial when it can't vanish on a subset of an integer grid. We prove its tropical version. Moreover, we establish a sharp bound on the number of points in a grid at which a tropical polynomial can vanish (for classical polynomials it is called Schwartz-Zippel lemma). We estimate the size of universal sets at which no tropical fewnomial (with a fixed number of monomials) can vanish. This relates to Erdos problem from convex combinatorial geometry. Finally, we produce two tropical versions of Shub-Smale's conjecture and show that one of them is true and another is false.

(jointly with V. Podolskii)

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/4234

[3] https://www.mpim-bonn.mpg.de/tropical2019