An application of algebra to topology

The theory of fusion systems is a new branch of mathematics with applications to finite group theory and algebraic topology. In particular, it is involved in a result in topology known as the Martino-Priddy Conjecture, which was proved recently by assuming the classification of finite simple groups.  New research with J. Lynd has used group theory to remove the classification from the proof.  I plan to describe fusion systems, the Martino-Priddy Conjecture, and open problems.