Invitation to asymptotic representation theory

Contact: Christian Kaiser (kaiser@mpim-bonn.mpg.de)

Asymptotic representation theory" studies (a) the representations of compact groups (for example, the symmetric groups S_n) in the limit when their size/dimension tends to infinity, or (b) the representation theory of "big" non-locally compact groups (such as the infinite symmetric group $S_\infty$). Often the traditional tools of representation theory and combinatorics are not useful for such problems; for this reason the asymptotic representation theory uses the tools of probability theory, harmonic analysis, ergodic theory, random matrix theory and some new "dual" combinatorial tools. During the talk we will see how these general ideas take a concrete form on a single specific example.