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.