# Weight conjectures for fusion systems

Note LRB

We will explain a result which shows that Alperin’s weight conjecture implies an equality between two natural numbers, each of which is a function of a pair (F,\alpha) where F is a saturated fusion system and \alpha is a compatible family of Kulsh\”{a}mmer-Puig classes in the system. The statement does not make reference to blocks, but if (F,\alpha) comes from a block, the natural numbers in question are supposed to equal the number of ordinary irreducible characters in the block. The result leads naturally to a variety of other counting conjectures for fusion systems.

This talk is part of the Algebra Seminar series.