Time: 5:00 pm
Location: Wean 8220
Title: Zariski Geometries. Part I
Abstract: The notion of a Zariski geometry was introduced by Ehud Hrushovski and Boris Zilber in 1993 in order to provide a non-algebraic characterization of the Zariski topology for algebraic curves using only topological properties and a well-behaved notion of dimension. Over the course of this work, it became apparent that Zariski geometries could be generalized to Zariski structures, which include not only higher-dimensional algebraic varieties, but also other geometric objects such as compact complex manifolds. Furthermore, this topological perspective, when combined with basic model-theoretic methods, yields interesting elementary results about a wide variety of structures.
The primary objectives of this talk are to introduce Zariski structures (with some geometric motivation) and to prove some elementary model-theoretic results about Zariski structures. This talk will follow Boris Zilber’s book Zariski Geometries (published 2010), which is currently available on his website at http://people.maths.ox.ac.uk/zilber/s.pdf.