Speaker: Marco Praderio Bova – Lancaster University
Abstract: Fusion systems are categories that, in a sense, represent an abstraction of the $p$-local structure of a finite group. Mackey functors on the other hand are algebraic structures with induction, restriction and conjugation operations satisfying certain properties that seem to appear in a variety of different contexts such as representation theory, group cohomology or algebraic K-theory among others. Mackey functors can be related to a variety of different constructions including fusion systems and, when related to fusion systems, they can be viewed as a pair of a covariant and a contravariant functors. In 2014 Diaz and Park conjectured that the higher limits of the contravariant part of any Mackey functor over a fusion system vanish. Such conjecture (known as sharpness for fusion systems) has seen a lot of recent activity, During this talk we will properly state such conjecture and overview the latest efforts made towards solving it.