Primary decomposition and differentiating by integers

Ponente(s): Jack Jeffries Jeffries, Alessandro De Stefani y Eloísa Grifo

The fundamental theorem of arithmetic states that every number can be written, in an essentially unique way, as a product of primes. A very similar result holds for polynomials in one variable. What about polynomials in many variables? A classical result of Lasker and Noether gives a generalization of this theorem to this setting. In algebraic terms (which we will define in the talk), it says that every ideal in a polynomial ring is an intersection of primary ideals. It is an interesting question to find geometric explanations for the primary ideals that show up in these intersections. A result of Zariski and Nagata gives an explanation for some ideals that show up in terms of calculus. In this talk, we will explain these classical results, and discuss some recent work that extends these results using a notion of differentiating by an integer. Las diapositivas para esta charla serán en español.