Harmeet Singh

The Hasse norm principle: degrees of failure

For an extension K/k of number fields, we say that the Hasse norm principle (HNP) holds if an element of k is a global norm whenever it is a norm everywhere locally. A really cool result of Bartels states that HNP holds for any extension of prime degree. In light of this, one can ask for which integers d does there exist a degree d extension of number fields failing HNP? In this talk, I will report on work in progress (joint with Gareth Tracey) answering this question, in particular reducing it to a problem in finite group theory.