Danny Gillam will give the talk on Monday, April 4 at 4:15 in Math 528. This lecture will be open to all.
Abstract: We address the following questions: Can a smooth curve be recovered solely by knowing the Zariski topology on each of its finite powers? What if we don't know the field it is defined over? What if the curve isn't smooth? Is there a purely topological means of differentiating smooth and non-smooth curves? Is there a purely topological characterization of the topologies on finite products of an infinite set that arise from a smooth curve? In addition to requiring a space to be noetherian, what other axioms do we need to build a reasonable dimension theory? Note that we will take a model-theoretic approach to these questions, though considerable algebraic geometry comes into play.
Return to the Elementary Methods Seminar Home Page.