|Location:||MSRI: Simons Auditorium|
There are a number of famous problems in the representation theory of finite groups. Examples are the McKay conjecture, the Alperin weight conjecture, Dade's conjectures and Brauer's height conjecture. Although considerable progress has been made on these problems, they remain open.
There are also a number of less well known open character-theory problems, mostly about solvable groups, and we will discuss a few of these in this talk. For example, it is still not known if normal subgroups of odd-order M-groups must be M-groups, or if it is possible in a noncyclic solvable group for the product of two faithful irreducible characters to be irreducible.