Speaker: Adam Chapman (Louvain) 
Title: Subfields of Quaternion Algebras.

Abstract:
This talk is based on a joint work in progress with Andrew Dolphin
(University of Antwerp).
We study the subfields of quaternion algebras.
Work had been done on this subject by Garibaldi and Saltman,
who gave an example of two nonisomorphic quaternion algebras
over a field of characteristic not 2 who share all their subfields,
and by Lam, who proved that if two quaternion algebras over a field
of characteristic 2 share an inseparable subfield
then they share also a separable subfield.
We provide examples of the following:
Two nonisomorphic quaternion algebras over a field of characteristic 2
that share all their subfields,
a quaternion algebra over a field of characteristic not 2
that shares all its subfields with another quaternion algebra
but not vice versa,
two quaternion algebras over a field of characteristic 2
that share all their inseparable subfields
but not all their separable subfields.