Rationality Problems in Algebraic Geometry

Rationality Problems in Algebraic Geometry

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Charlie Stibitz, Princeton University
Fine Hall 110

A long standing problem in algebraic geometry is to understand when the solutions to polynomial equations can be rationally parameterized by an affine space. Even for smooth hypersurfaces the problem remains open in many cases. This talk will give an introduction to different variants of rationality, examples of when they are or are not satisfied, and some of the methods used to prove nonrationality in these cases. If time permits, we will discuss some applications to families of varieties.