Quantifying Ramification of Representations
Irreducible representations of compact Lie groups can be classified in terms of highest weights, and one can use this to give a natural ordering of these representations. I will discuss the analogous problem of quantifying the complexity of a representation of a noncompact group over a local field. This problem is well-understood for representations of the general linear group over nonarchimedean fields, but little is known for the corresponding archimedean problem. I will highlight how a resolution of this problem has applications towards evaluating integrals involving automorphic forms.
Dr Peter Humphries, University College London