## The genus of a division algebra

#### Igor RapinchukHarvard University

In this talk, I will address the following problem. Suppose $D$ and $D'$ are central division algebras over a field $K$. What can be said about $D$ and $D'$ if they have the same maximal subfields? I will discuss various motivations for this question and recent results. This is joint work with V.~Chernousov and A.~Rapinchuk.

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