| Résume | Representation theory studies symmetries of linear algebraic objects; it has been connected to geometry from its inception, since symmetries of a geometric space X produce symmetries of the linear space of functions on X. However, less direct, "hidden" connections of representations to geometry have lately been playing an increasingly important role in the subject. I will talk about some such connections, describing examples where irreducible representations can be counted by counting Betti numbers of a (surprisingly) relevant space, while their structure can be (partly conjecturally) related to geometry of Lagrangian subvarieties in (an even more surprisingly) relevant symplectic manifold. |
