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Mathematics Colloquium

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Date:  Tuesday, February 03, 2015

Title:  Recent upsets in some rationality problems

Abstract:  The problem of determining whether a given finitely generated field extension is purely transcendental, or rational, has confounded mathematicians for generations, stimulating major advances in topology, algebraic K-theory, and algebraic geometry. I will touch on two types of rationality problems, both of which have witnessed intriguing upsets in the last couple years. First, Noether's problem, posed in 1913, asks if the field of invariants of a finite permutation group acting on a set of algebraically independent variables is rational over the base field. Here, I will discuss some intriguing developments in the case of p-groups. Second, the rationality problem for (function fields of) cubic hypersurfaces in projective space has a beautiful history, and is still open in the 4-dimensional case. Here, I will discuss recent upsets to certain conjectural approaches to the problem.


Speaker:  Asher Auel
Institution:  Yale University

 

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