Global properties of period maps at infinity
Friday, 3.6.22, 10:30-11:30, Hörsaal II, Albertstr. 23b
Orbit Method: From Matrices to Unitary Representations
Tuesday, 14.6.22, 10:30-11:30, Raum 218, Ernst-Zermelo-Str. 1
The talk is intended as a leisurely introduction to one of the fundamental tasks of representation theory: the construction of irreducible unitary representations. I will first discuss two major sources of unitary representations of Lie groups, one from Symplectic Geometry (Kirillov theory) and another from Number Theory (Arthur’s conjecture). I will then introduce a constructive method called theta lifting which has been fruitful for representations of classical groups and discuss some recent applications of this method to unitary representation theory.\n
The derived category of permutation modules
Friday, 24.6.22, 10:30-11:30, Hörsaal II, Albertstr. 23b
To a field k and a finite group G one associates the derived\ncategory of kG-modules, an important invariant that is difficult to\nunderstand in general. At least, its tensor-triangulated structure\nadmits a familiar description in terms of the support variety.\n\nWe propose to study a refinement, the derived category of G-permutation\nmodules over k. It has interesting interpretations in algebraic\ngeometry, representation theory and equivariant homotopy theory. We\nwill say a few things we know about its tensor-triangulated structure. \nThis is based on joint work, mostly in progress, with Paul Balmer.