Danny Gillam will give the talk on Monday, February 14 at 4:15 in Math 528. This lecture will be open to all.
Abstract: We will discuss a proof of the nullstellensatz using techniques from the model-theory of first-order logic. In particular, we study the theory of algebraically-closed fields (of a fixed characteristic) in the language of rings, and prove (or quote the fact that) it admits quantifier elimination. The nullstellensatz and Chevalley's theorem follow trivially. We'll at least define all these terms in the talk. The methods are elementary in the sense that the hardest actual theorem we need to quote is Hilbert's basis theorem, though we'll probably quote quantifier elimination for ACFp without proof.
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