# Geometria em Lisboa Seminar

### 10/12/2015, 16:30 — 17:30 — Room P3.10, Mathematics Building

Edgar Costa, *Dartmouth*

### Equidistributions in arithmetic geometry

Consider an algebraic variety defined by system of polynomial equations with integer coefficients. For each prime number $p$, we may reduce the system modulo $p$ to obtain an algebraic variety defined over the field of $p$ elements.

A standard problem in arithmetic geometry is to understand how the geometry of one of these varieties influences the geometry of the other.

One can take a statistical approach to this problem.

We will illustrate this with several examples, including: polynomials in one variable, algebraic curves and surfaces.