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Conjectures in local representation theory

Presented by: 
Charles Eaton
Friday 10th January 2020 - 11:30 to 12:30
INI Seminar Room 1
I will survey the principal conjectures concerning the local determination of information about blocks of finite groups. Local determination, meaning determination from information about p-subgroups, their normalizers and related subgroups, has been a significant strand of the subject since Brauer. In some cases we can already tell a great deal about a block even from just the isomorphism type of its defect groups. Much of the recent activity around block theory revolves around a number of conjectures predicting precisely how invariants are determined from local subgroups. These invariants range from simple numerical invariants such as the dimension of the centre to the equivalence class of the module category and related categories.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons