A lecture by Jean-Pierre Demailly of CNRS, Grenoble.

Algebraic geometry is the art of solving polynomial equations. Greek mathematicians already considered "Diophantine equations", which consist of finding integer or rational solutions. It turns out that this problem is deeply connected to the geometry of the set of complex points and to the existence of entire analytic solutions, and is usually governed by the degrees of the polynomials involved. We will describe informally some recent results on these questions.

https://www.sissa.it/news/sissa-colloquium-analytic-and-arithmetic-solutions-algebraic-equations