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September 25, 2015
Friday, September 25
Algebra Seminar
Time: 14:30
Speaker: Cam McLeman (University of Michigan - Flint)
Title: "Old and new invariants in the class field tower problem"
Room: MC 107

Abstract: Given a number field, we form the Hilbert p-class field tower by repeatedly iterating the Hilbert p-class field construction. Work of Golod and Shafarevich demonstrated that this construction can fail to stabilize after finitely many steps, and the slew of natural questions that this observation unleashed remain largely unanswered. In particular, there is no known definitive criterion for deciding if a number field has an infinite such tower. In the case of quadratic imaginary number fields, however, we are close to honing in on a set of invariants which completely resolve the question. This talk will cover both historical such invariants and modern ones, giving the current status of our ability to determine the infinitude of such towers.