Title : Obstructions to Noether's problem
Speaker: Primoz Moravec
Affiliation: University of Ljubljana
Time: 4:00 pm Thursday, 30 November, 2017
Location: 303-B05
The Bogomolov multiplier is a group theoretical invariant isomorphic to the unramified Brauer group of a given quotient space, and represents an obstruction to Noether's problem on rationality of fixed fields. It has also appeared implicitly in K-theory, topology and mathematical physics. We will survey some recent results regarding Bogomolov multipliers and their higher dimensional analogs, the unramified cohomology groups. We describe how Bogomolov multipliers detect universality of commutator relations in groups. We prove a Hopf-type formula, and describe the role of the Bogomolov multiplier in the theory of central extensions. An algorithm for computing the Bogomolov multiplier will be outlined, along with an algorithm for computing certain subgroups of the third unramified cohomology groups in some particular cases.

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