#### Conference abstracts

Session A2 - Computational Algebraic Geometry

July 11, 14:30 ~ 14:55 - Room B5

## Factorization of sparse bivariate polynomials

### MartÃn Sombra

### ICREA & Universitat de Barcelona, Spain - sombra@ub.edu

It is expected that, for a given sparse univariate polynomial over the rationals, its non-cyclotomic irreducible factors are also sparse. This is a vague principle that takes a more precise form in an old (and still open) conjecture of Schinzel, on the irreducible factors in families of polynomials with fixed coefficients and varying monomials.

In this talk, I will present a theorem giving an analogue of Schinzel conjecture for polynomials over a function field. This result gives a description of the irreducible factors in families of bivariate polynomials over a field of characteristic zero.

Its proof is based on a toric version of Bertini's theorem.

Joint work with Francesco Amoroso (UniversitÃ© de Caen, France).