# Master's Student Learning Seminar

#### 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, **k**^{n}, and structured subsets of our algebraic structure **k**[X_{1}, . . . , X_{n}]. More specifically, we can establish a correspondence between affine algebraic subsets V of **k**^{n} and certain ideals I of **k**[X_{1}, . . . , X_{n}]. The upshot is that this lays the groundwork for the further development of modern algebraic geometry.

**Notes:**