Pure Maths Colloquium: 'Say XxA^1=A^n. Please solve for X'...and related questions
3 November 2008 16:15 in CM221
The problem of the title in Algebraic Geometry is known as the Zariski Cancellation Problem. In this talk, we approach it from a variety of perspectives -- smooth manifolds, algebraic varieties, and birational geometry. En route we encounter an historic misproof of the Poincare conjecture, classification of contractible manifolds, a characterization of algebraic families of vector bundles, a reinterpretation of singularities, and some fun with spheres. The goal is to extract as much algebraic geometry as possible from what are essentially motivic -- er, topological -- ideas. This is drawn from joint work with Aravind Asok, and also Francis Kirwan. Pretty examples abound.
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