P. Diaconis and M.Isaacs constructed a supercharacter theory for algebra groups, of the form G=1+J (with J a nilpotent algebra over a finite field), in order to gain a better understanding of the irreducible characters of G. Later, M.Boyarchenko and V.Drinfeld defined Character Sheaves for unipotent groups with the same goal. In this talk, a definition of Supercharacter Sheaves motivated by the work in character sheaves will be given, together with some of the results obtained. In particular, the results from the paper of P. Diaconis and M.Isaacs will be translated for the setting of Supercharacter Sheaves.
