turkmath.org

Since their appearance fusion systems have received much interest in both algebra and topology and in 2011 Asbacher, Kessar and Oliver published a list of problems involving fusion systems many of which remain nowadays open. One of such problems was rephrased in a more general way by Díaz and Park in 2013 and has since been known as the sharpness for fusion systems conjecture. This conjecture has seen a lot of activity in recent years. During this talk we will briefly go over the concepts of fusion system and Mackey functor, use those in order to properly state the sharpness conjecture, mention the results we know involving this conjecture and finally sketch the proof that the Benson-Solomon fusion systems (the only known family of exotic fusion systems over 2 groups) satisfy this conjecture.