Mathematical Sciences Seminar for Master's Students

Hilbert's Nullstellensatz and some Applications.

Speaker: Antonios-Alexandros Robotis, CIMS

Location: Warren Weaver Hall 1314

Date: Wednesday, October 25, 2017, 7:10 p.m.

Synopsis:

The purpose of this talk is to provide a fairly simple proof of Hilbert's nullstellensatz. Nullstellensatz is a German word, roughly translating to "zero locus theorem." As such, the nullstellensatz ensures a correspondence between special subsets of our geometric space, kn, and structured subsets of our algebraic structure k[X1, . . . , Xn]. More specifically, we can establish a correspondence between affine algebraic subsets V of kn and certain ideals I of k[X1, . . . , Xn]. The upshot is that this lays the groundwork for the further development of modern algebraic geometry.

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