### Dual spaces and Noetherian operators

- Series
- Student Algebraic Geometry Seminar
- Time
- Monday, February 17, 2020 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Marc Härkönen – Georgia Tech – mharkonen3@gatech.edu

Noetherian operators are a set of differential operators that encode the scheme structure of a primary ideal. We propose a framework for studying primary ideals numerically by using a combination of witness sets and Noetherian operators. We will also present a method for computing Noetherian operators using numerical data.

The first step in the theory of Noetherian operators are the Macaulay dual spaces. Indeed, for an ideal that is primary over a maximal ideal corresponding to a rational point, the generators of the dual space are a valid set of Noetherian operators. We will start by presenting basic ideas, results and algorithms in the classical dual space theory, and then revisit some of these ideas in the context of Noetherian operators.