Speaker: Darren Semmen
Title: Duality groups and modular towers

Abstract : The difficulty in proving the regular version of the Inverse Galois Problem would be explained by the (conjectural) disappearance of rational points on high levels of any modular tower. It is already known that there are no projective sequences of rational points, so part of the current strategy to prove this conjecture is to characterize infinite sequences of components. Rephrasing obstruction (i.e. having no components at higher levels mapping to a given Hurwitz space component) and branching (i.e. having more than one) in terms of cohomology introduces the use of duality groups to the problem.