Conferencia de Francesco Russo

El jueves 26 de marzo , Francesco Russo (Universidad de Catania) dictará la siguiente conferencia:

Título: When can we parametrize algebraically the solutions of (a system of) polynomial equations?

Resumen: To find explicitly all the solutions of a (system of) polynomial equation(s) is a central problem in mathematics, appearing in all areas of research.

When the equations are all linear, we all know the answer independently of the field and of the number of variable. Moreover, everybody is able to pamatrize linearly (and hence algebraically) all the solutions in terms of some variables.

When the degrees of the polynomials are greater than one, we need some assumptions on the field or on the number of variables to get similar results. For example we can parametrize algebraically all the solutions of equations of degree two as soon as we find at least one solution in the base field (which cannot exist in principle).

We shall give necessary conditions on the existence of an algebraic parametrization (not necessarily bijective) of the solutions in terms of the degree of the equations (degree less or equal than the number of variables) and we shall show that as soon as the number of variables is at least three this condition is far from being necessary in contrast with the case of one or two variables. We shall conclude by showing the consequences from a computational point of view of these results, the connections with some results in arithmetic like Fermat Last Theorem and we shall briefly outline some of our contributions in the field.

La exposición y las herramientas utilizadas serán elementales y la mayor parte del contenido será accesible también para estudiantes de posgrado.

Fecha, hora y lugar: jueves 26 de marzo de 2026, a las 10:30 en el salón de seminarios del piso 14 del Centro de Matemática de la Facultad de Ciencias.