In this talk we will focus on two-variable polynomials restricted to rational numbers f:QxQ -> Q.
We will introduce some open problems related to these maps, and how they relate to other topics in arithmetic algebraic geometry.
For example, whether there is such a map that is injective or that is bijective is an open problem, and both have only been answered conditional to the Bombieri-Lang conjecture. Speaker(s): Jose Esparza Lozano (UM)